(FORTUNE Magazine) - To hear Ed Breen tell it, splitting his company in three is the most natural thing in the world.

On this late February day, the CEO of Tyco International (Research) is sitting in a conference room in the company's New York outpost, two blocks from the regal former seat of his disgraced predecessor, Dennis Kozlowski. The 50-year-old Breen, who comes across more like a friendly dad in a 1950s TV series than an imperial chief executive, cheerfully ticks off reasons it makes sense to rend the $40 billion conglomerate into pieces. "Flexibility" is one that he cites; also "clarity," "focus," and giving the units "their own currency."

In his first interview since the announcement on Jan. 13, Breen insists that a breakup was always a possibility; he's taking the step now, he says, because Tyco has "reached a demarcation point." The company has recovered its financial health and reputation, he explains, so it's now free to let its divisions--health care; fire and security and engineered products; and electronics--leave the corporate nest; they'll fly highest on their own. "It's the best way to create long-term shareholder value at the company," Breen says. "I really stress long term, because I'm not looking for some overnight pop here."

It all sounds so benign and reasonable that it's easy to just nod. And yet a question keeps bubbling up, one that could be reduced to a single syllable: Huh?

Wasn't Tyco the outfit that, after overcoming its recent troubles, was proving that conglomerates could work? When FORTUNE last wrote about the company, in November 2004, we approvingly noted that "Tyco's goal is to become another GE (Research)." Breen had restored the shine that Kozlowski's crimes and excesses--is there anyone now who doesn't know about the $6,000 shower curtain?--had so tarnished. Yet little more than a year later, here is Breen matter-of-factly discussing its dismantlement--with a plan that is disconcertingly similar to one that imploded when his predecessor attempted it four years ago.

Perhaps Breen deserves the benefit of the doubt. After all, he saved Tyco from a life-threatening liquidity crisis and chopped debt to just over $10 billion today from $28 billion in 2002. During that same period Tyco's free cash flow has exploded, from $800 million to $4.6 billion. For a while its stock was even making investors rich again, rising from $8 to a high of $36 in 2-and-a-half years.

But during the past year the turnaround has stalled, and Tyco has squandered much of the goodwill and credibility it had recovered. The company has failed to meet Wall Street's expectations in four of the past five quarters, driving the stock back down to $26. Only seven of 17 analysts who cover Tyco rate it a buy, according to Thomson Financial, despite its prodigious cash generation and below-market P/E of 14. Analysts are so dubious about the company's earnings guidance for this year that their consensus estimate is below Tyco's own projections.

Certainly Tyco still has a retinue of glamorous fans, including money managers such as Bill Miller of Legg Mason Value Trust, who bought millions of shares of Tyco when most investors were running for the hills. Indeed, you could assemble a Value Investors Hall of Fame out of those who have acquired Tyco shares in recent years: Miller, Chris Davis of Davis Advisors, Leon Cooperman of Omega Advisors, Wally Weitz of Weitz Funds, Robert Olstein of Olstein Funds. Tyco shares have even turned up among the holdings of Berkshire Hathaway (Research). Several of these famously patient investors, whose investment horizons can stretch over decades, have been loading up more in the past few months. (Another famed investor, one not noted for his patience, has entered the mix: Carl Icahn bought two million shares recently.)

But not one of these players has been pushing Tyco to carve itself up. (Some of them have been agitating for Tyco to buy back more shares in an effort to lift the stock price.) That doesn't mean Breen's breakup plan is a mistake. On the other hand, even the maneuver's defenders acknowledge that it will have no effect on the company's recent operational snafus. "It doesn't fix it," says Leon Cooperman. "The breakup isn't the solution to their problems. The solution is to do a better job of managing the company."

Tyco's image has oscillated wildly in the past five years. It's been a fast-growth, acquisition-minded company with a superstar CEO, Dennis Kozlowski; a scandal-tarred, debt-laden corporate invalid with an indicted ex-CEO (also Kozlowski); and a scrappy fighter regaining respectability and responsibility.

Through it all, the vast majority of observers have agreed that Tyco has an outstanding collection of businesses. Today the company's 2,000-plus legal entities make everything from electronic security systems to diapers; from metal conduit and industrial valves to pharmaceuticals; from sprinkler systems to printed circuitboards and medical imaging equipment.

Kozlowski might have assimilated them in slapdash fashion--and the company certainly took liberties in accounting for the acquisitions--but most generate copious amounts of cash. That's why, even during the company's darkest hours, astute investors never confused Tyco with Enron or WorldCom. That's why the Bill Millers of the world have held on during a sometimes bumpy ride, and that's a large part of what lured Breen to the company from his perch as CEO-in-waiting at Motorola (Research).

Indeed, Breen's mantra--that Tyco is the conglomerate that can't get any respect from the market--is little different from what Kozlowski was saying in January 2002. At the time, the company's once-roaring stock had started to fall in the wake of questions about its accounting. Then Kozlowski's proposal to split Tyco into four pieces sent the stock reeling. By the time Kozlowski scotched the breakup plan in April 2002, the shares had fallen to $19.90 from the $46.40 they traded at the day before the split-up was announced. Tyco's credibility was shot. (Soon after, Kozlowski was on the path to an 8-to-25-year sentence in a New York State prison for looting millions from the company.)

When Breen arrived in the summer of 2002, a huge liquidity crisis loomed, with some $11 billion in debt coming due in 2003. He valiantly found a way to refinance the debt--a key victory in a campaign that eventually purged Kozlowskianism from every corner of the enterprise. He pushed out all the directors and replaced them with independent outsiders. He fired 300 senior managers and created new corporate governance mechanisms to prevent future shenanigans. He decamped from Tyco's lavish New York City offices and moved the corporate staff to modest digs in suburban New Jersey. Breen shuttered redundant factories, slashed costs, and restated more than $1 billion of tainted Kozlowski-era earnings.

What Breen didn't do, however, was tamper with the essential makeup of the company. If he was considering the idea of separating Tyco in the future, it certainly wasn't something he was discussing publicly. As he told the Wall Street Journal one year into his tenure, he was happy with Tyco's collection of assets: "One of the things that I liked about Tyco--and studied hard before coming in--was its ability to generate cash. The company had great businesses. They were in the right sectors. The foundation was very strong." The problem, he explained, was corporate governance and trust.

In effect, Breen's goal was to heal the existing organization, not to perform radical surgery on it. As he wrote to shareholders in Tyco's 2003 annual report, "Our strategic plan, which we began implementing in 2003, is to grow Tyco organically--by increasing business volume, gaining market share, and improving operating efficiency."

The wisdom of Breen's approach became apparent in 2004. With Tyco's free cash flow quintupling and debt cut to a manageable level, the bond-rating agencies restored its investment-grade status. The stock surged, and with the operations humming along, Breen even began broaching the notion of--could it be?--new acquisitions. Breakup seemed the last thing on his mind. During a conference call in November 2004, Breen announced that the company had nearly completed its divestiture program, shedding $1.5 billion worth of underperforming smaller businesses. When an analyst asked if he planned any big divestitures, Breen responded, "No, there are no big ones coming."

Then the troubles began. As 2005 progressed, each of the company's main divisions encountered operational problems and eroding profit margins. For Tyco's $12 billion electronics unit, the cause was rising copper and gold prices (the company buys 200 million pounds of copper each year, according to a Merrill Lynch report, and 300,000 ounces of gold). Later in the year Tyco's jewel--its $10 billion, high-margin healthcare unit--was on the spot. It recalled three imaging products, one of them--NeutroSpec, an agent that can be used to diagnose appendicitis--after two patients died.

Serious, yes. But these were not failures of corporate strategy. It's hard to see how Breen's executive team in New Jersey was responsible for, say, high copper prices. And Tyco was far from a financial fiasco; it boosted earnings 13% in 2005 and generated billions in free cash flow.

Yet that wasn't quite enough for an investment community primed for good news. One problem: Much of Tyco's earnings improvement in 2005 was fueled by cost cuts, lower interest expense from paying down debt, a better tax rate, and the like. Tyco's organic growth--a measure Breen often emphasizes--had dropped from 5% in 2004 to 3%.

"Tyco's core fundamentals in '05 were abysmal versus peers," wrote Morgan Stanley analyst Scott Davis in December. Investor Cooperman lectured Tyco executives on a conference call: "The problem, frankly, has been execution."

Worst of all, perhaps, Tyco violated a sacred commandment in the investing world: Thou shalt not underperform Wall Street's expectations. Indeed, Tyco has now broken that rule not once, but four times in five quarters. You can sense the annoyance among analysts. Citigroup's Jeffrey Sprague, for example, titled a recent report "Groundhog Day--Another Disappointment."

In a February conference call, one analyst even pleaded with Tyco's management to lower its guidance. Deutsche Bank's Carter Shoop took issue with the company's prediction that the cost of raw materials would stabilize. "Why don't we be a little bit more conservative?" he asked. "Maybe lower fiscal year '06 guidance altogether, and assume that these price increases that have been going on for two or three years continue.... Take the medicine now, see the stock price sell off a little bit more today [rather than face the] probability of having to reduce that '06 guidance at a later date, which would be a negative event for the stock." Responded Tyco CFO Chris Coughlin: "We're comfortable" with our projections.

Since Tyco won't lower the guidance, says Goldman Sachs analyst Jack Kelly, "the Street has kind of lowered the guidance for them." He notes that it's unusual for analysts to coalesce around an estimate that is lower than the company's range. "That's why the sentiment on the stock is so negative." (Analysts expect fiscal year '06 earnings of $1.83 per share; the company has pegged them at $1.85 to $1.92.)

Unmet expectations have chiseled away at the stock price. Shares did climb in November, when Breen hinted that a split-up might be in the offing. But when Breen made it official in January--at the same time also disclosing an earnings miss--the market's reaction was swift. Tyco's stock price dropped $3 to $27 on the news, then settled under $26 in the weeks afterward.

Coming with the earnings miss, the announcement of the breakup plan has led some Wall Street analysts--most of whom endorse the proposal--to conclude that management doesn't have any better ideas for fixing the company. "They did a terrific job of recapitalizing the balance sheet and paying off a substantial amount of debt, improving the cash flows, and improving the overall profitability," says Merrill Lynch analyst John Inch."They picked off some low-hanging fruit. But the question now becomes, Have they run into a wall?"

S&P debt analyst Joel Levington is even harsher. "It feels like there's some financial razzle-dazzle that's going on," he says. "They're turning the attention of investors toward the financial-engineering aspect of their strategy, as opposed to what really needs to be done, which is to continue to work on the basics and get their revenues and their margins back up."

Ed Breen dismisses these criticisms. In his view, the separation plan is completely unrelated to Tyco's recent operational problems. Well, maybe not entirely unrelated. He disputes the idea that Tyco's current structure is hampering the individual units but then goes on to suggest that as independent entities, they will be better able to grow.

Breen can be disarmingly candid and willing to shoulder responsibility. For example, he's quick to emphasize that Tyco's recent earnings miss was a result of "mostly our own internal issues--not the marketplace." Certainly the breakup plan itself, which will take Breen from being the CEO of a $40 billion enterprise to heading an $18 billion operation (Tyco's fire and security and engineered-products businesses) hardly suggests the plotting of an egomaniacal CEO.

The separation plan, Breen says, emerged in large part because the company had reduced its once-crushing debt. "That was not the No. 1 focus anymore," he says. And so, beginning in the spring of 2005, management began exploring whether the company should sell a unit--the health-care division was the leading candidate--perhaps make an acquisition, or even split itself up.

Considering spinoffs and restructuring was a luxury that Tyco simply hadn't had for years, says Jack Krol, the company's lead director and a former chairman of DuPont (Research). "When I came in with Ed," he says, "my view and the board's view was that we had three things to do: save, fix, and grow."

Tyco's liquidity crisis and the scandal-related legal and image problems made it impossible to consider a more substantial restructuring. Still, he and Breen insist it was always in the back of their minds. "I remember the first day I was with Ed," says Krol, "and he was trying to talk me into coming on this board. I said to him, 'One of the questions that we're going to have to face is, Why is all of this stuff together?' "

By last fall, Tyco's management and board, with assistance from consultants at McKinsey, had narrowed the options to two: Keep the company in its current form, or split it up. Tyco then brought in two squadrons of investment bankers. First, Goldman Sachs made the case for separation. Then the board asked Evercore Partners and Rohatyn Associates to argue for preserving the structure.

Tyco's dream of conglomerate glory did not die quickly, says Krol. "There were a lot of board members saying, 'Well, wait a minute now, why can't we be another GE?'" But over the months the Goldman presentation convinced the board that the units would grow faster apart than together.

The good-natured Breen comes as close as he can to bristling when asked about the notion of financial engineering. "That's just absolutely not the case," he says, pointing out that the company began debating its structure before most of the business disappointments. "We were running great. We get a couple of quarters where we're not running where we should be. We'll get over that and start performing where we should be in the second half of the year." He says he would never make a short-term move to goose the company's shares. "Over time," he says, "the stock takes care of itself."

For now Tyco's stock price still seems to be affected as much by its history as by its fundamentals. It's safe to say that with or without the spinoff, Tyco will continue to generate boatloads of cash, and with or without the spinoff, it will need to continue attacking both the remaining Kozlowski-era bloat and its operational challenges.

"Maybe people were a little premature thinking that Breen had fixed everything," says value fund manager Wally Weitz, who has been a recent buyer of Tyco shares. "It's just sort of a harder job than people realized."

The obvious question is: Will a three- way split make the job easier? It's impossible to know. You certainly can't argue against greater focus and flexibility. The stocks of recent spinoffs such as Genworth Financial have far outpaced their parents' (in Genworth's case, GE), notes analyst Davis of Morgan Stanley.

Adds Jeff Bronchick, the chief investment officer of money manager Reed Conner Birdwell (whose largest holding is Tyco): "I know the health-care people inside Tyco are referring to this as Operation Freedom." Once liberated, the theory goes, they will be better able to tackle their own problems. That said, if Tyco's corporate group--Breen, et al.--hasn't been the problem, will removing them be the solution? How will that fix, say, quality problems at a Tyco plant that makes respiratory-care products in Juarez, Mexico (another recent trouble spot)?

Tyco shareholders will need to wait at least a year to see the next chapter. That's how long it will take to untangle Tyco's 2,200 subsidiaries, not to mention wrap up its unresolved Kozlowski-era SEC investigation and get closer to settling its shareholder litigation. The estimated tab for the unwinding: a whopping $1 billion. (The breakup's defenders note that it's the equivalent of a relatively modest 50 cents a share.) In the meantime, if one of the long-term benefits is that management attention will be less stretched among different units, the opposite is true in the short term: Breen will be trying to rectify problems in operating units even as he oversees his company's dissolution.

In the end, though, the biggest advantage of a breakup might be a seemingly minor detail: the company name. Tyco has studiously avoided any mention of what the three entities will be called. This, of course, is a perfect moment for the units to create new identities free of a cloud that has never quite lifted. It's testament to the fact that even in 2006, the key name here isn't Breen or even Tyco--it's still Kozlowski.

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REPORTER ASSOCIATE Joan Levinstein contributed to this article.