(FORTUNE Magazine) – Jeffrey Immelt must be having that Phil Bengston feeling right about now.

Phil who? you ask.

Our point exactly. Some leaders are remembered for their wisdom, others for their exploits, but no one remembers the man who succeeded Vince Lombardi as coach of the Green Bay Packers.

As Immelt, 44, prepares to take the reins of the corporation that's both the most valuable and most admired in the world, he may be following an even tougher act. About the worst thing said of Jack Welch these days is that he's the 20th century's second-greatest manager (after Alfred P. Sloan of General Motors). "Immelt will be in the shadow of the Sun King," says Bennett Stewart of consulting firm Stern Stewart. The career of the Sun King's successor, Louis XV, whose ineffectual rule helped pave the way for the French Revolution, isn't very encouraging on this score. Nor is recent corporate history: At Coke, Douglas Ivester was quickly deemed an unworthy heir to the deified Roberto Goizueta. And so as Immelt's defeated rivals parachute into the top jobs at 3M and Home Depot with the chance to be heroes, the question arises: Has Immelt snared the best job in business? Or, like the dog that finally catches the car, has he snared the worst?

"I'm not sure I would take the job," muses James Collins, co-author of the business bestseller Built to Last. "It's very common for legendary CEOs to depart and for their successors to have great problems."

If such talk unnerves him, Immelt showed no sign of it as he sat down with FORTUNE at GE's leadership center in Crotonville, N.Y. The chairman-elect was relaxed, confident, even effusive. "Running GE is just not something that scares me," he said. "I feel this is the first day of my career....I feel like it's all ahead of me--you know, just being reborn and just totally energized about doing it. I guess I should be scared, but I don't feel that way."

A good thing, considering the expectations being heaped upon him. Just how great are they? GE's $53 stock price may provide the best answer. According to an analysis by Stern Stewart, 82% of that price is based on investors' hopes for future earnings growth, rather than on GE's fundamentals. (For more on this methodology, see "America's Best and Worst Wealth Creators," Dec. 18, in the fortune.com archive.) In other words, if GE were merely to sustain its unprecedented level of profitability, investors would be willing to pay just $9.50 for its stock--18% of what they're paying now. "When you see market-value premiums like that, you have to shake your head," says Stewart. "The success of GE has established an expectation for future growth so enormous that I don't even know if Jack Welch could accomplish it."

Whether that's fair or not is mostly beside the point. The point is, over the past two decades there have been a handful of certainties: Cal Ripken played shortstop for the Baltimore Orioles, Dick Clark hosted New Year's Rockin' Eve, and Jack Welch delivered ever-higher earnings per share at GE. End that streak, and investors won't let you forget it.

So where does Immelt begin? First, remember that Elvis has not left the building. So while Welch sticks around for the next year overseeing the Honeywell merger, Immelt can figure out what to do with Welch's legacy. "It's not his shoes you have to fill, it's your shoes," advises leadership expert Warren Bennis of the University of Southern California. Complicating this task will be the fact that Welch's legacy is all about destroying legacies. To wit, one of his first acts as CEO was to undo the biggest deal of his predecessor's career, GE's purchase of the mining company Utah International. Welch outraged sentimentalists by selling GE's housewares business; dumped the long-standing organization by "departments"; eliminated more than 100,000 jobs; and generally disregarded the principles in the Blue Books, a five-volume set of codified management technique given to every GE manager. (To spare Immelt the moniker "Neutron Jeff," Welch may yet drop one final downsizing bomb: Analysts expect as many as 30,000 job cuts from Honeywell.)

Immelt, then, may be inheriting a corporate icon, but he's also inheriting a long tradition of iconoclasm. He hasn't said how he might resolve that paradox. Revamping GE's culture seems unlikely, since it's among the most effective on earth. And Welch's four big initiatives--services, globalization, e-business, and the quality-management program known as Six Sigma--are far from played out. But a reshuffling of GE's portfolio could be in the cards. Already there is pressure to unload the low-margin appliances business, as well as NBC, which some fear could lose its perch as the No. 1 network if it doesn't link up with a big entertainment company. "Over time, [Immelt] will have to reinvent GE just as Welch did," says Larry Bossidy, the former GE executive and retired Honeywell chairman. "People don't think GE needs fixing now, but they didn't think it needed fixing then either."

Most formidable, though, is Immelt's long-term challenge: to continue to defy the laws of economics. A collection of 20 largely unrelated businesses, GE resembles the conglomerates that stalked the earth in the 1960s and 1970s but are now extinct. The reasons for their disappearance aren't a matter of debate anymore: Managers couldn't allocate capital better than the market could; cash flow from strong divisions was used to prop up weak ones; investors looking for diversification could simply buy a mutual fund. Plus, there was only one stock to give employees, which "is like issuing one report card to a whole class of students," says Stewart. All of which would seem to assert the impossibility of GE's existence. Yet there it is--a splendid, colossal exception producing $12 billion-plus a year in profits.

This anomaly has occupied the explanatory powers of a whole generation of management gurus and analysts, all desperate to divine the ingredients of the secret sauce. How, they wonder, can anyone manage an empire of such complexity?

The answer may be that GE doesn't "manage" its disparate businesses at all. "Welch doesn't know crap about making jet engines or doing CAT scans," argues Noel Tichy, a University of Michigan professor who once ran Crotonville and who co-authored the GE book Control Your Destiny or Someone Else Will. Rather, the CEO functions more like gadfly-in-chief, spreading best practices, driving key initiatives, and enforcing strict performance goals. To the extent that he delves deeply into particular businesses, it's to make broad decisions about where to invest capital and talent. Asked what GE's core competency is, Immelt responds: "We pick great people, we make them better, and we retain them." So it may be that GE--which will comprise about half a percent of world economic output once it swallows Honeywell--is best viewed not as a company, but as an economy unto itself, a place where the capital is smarter, the pockets deeper, and all managers are above-average.

But like Yugoslavia after Tito, GE must now contend with powerful centrifugal forces that have caused more than one large company to fly apart in a blaze of tracking stocks and spinoffs. The new-economy fetish for "pure plays" tends to value huge combines like GE as less than the sum of their parts. And one wonders if GE's vaunted system of rotating managers through jobs to create skilled "generalists" is quite so attractive in a world where job-hopping is easily done on one's own, often via the Internet.

Welch--who began his tenure as Neutron Jack but is finishing it as Electron Jack--has done a remarkable job of using the Net to strengthen GE's effectiveness, asking employees, for instance, to "Webify" their jobs to strip out billions in costs. "There is no such thing as the new economy," argues Immelt. "What you really have is a transformational technology that is right in our sweet spot." Still, Immelt will be in a race to harness the powers of the new economy faster than those same forces can rip GE apart.

The key question, of course, is how much of the secret sauce consists of Welch himself. His admirers like to call GE "the house that Jack built." But there are also reasons to see him as just one in a distinguished line of tenants. Consider, for instance, what FORTUNE wrote at the time of his succession: "The trick will be to make changes without damaging the reputation for stability, predictable earnings increases, and sound management that have characterized the company in recent years. That reputation is the major achievement of Welch's predecessor, Reginald H. Jones." Courtly and statesmanlike, Jones was overwhelmingly selected as America's most admired CEO in a FORTUNE poll.

He wasn't the first luminary to occupy the office either. GE's six previous chiefs were all among the great managerial innovators of their day, lasting 14 years on average. GE's average return on equity under Welch--29%--is impressive, but not as good as the numbers put up by three of the four previous CEOs: Jones, 29.7%; Fred Borch, 27.5%; Ralph Cordiner, 40.4%; Charles Wilson, 46.7%. "[Welch's] is not a singularly outstanding performance," says James Collins, who compiled the data.

Collins' point is not to diminish Welch, but to note that GE's famed system for developing management talent runs far into the past and deep into the organization. "I see Welch much more as a product of GE than GE as a product of Welch," he says. And while it's true that the company Welch inherited was in need of a good shaking--GE was described then as a bureaucracy "with its face to the CEO and its ass to the customer"--perhaps the ultimate proof of its greatness is that it chose Welch, a relative unknown with a reputation for impetuousness who would have been buried at most companies. "Here was this short, stuttering guy who only knew the plastics business," recalls a former GE executive. "Everyone was saying, 'Ohmigod.'"

Immelt, by contrast, begins his tenure in almost universal high regard. "This is a superior brain," says Ram Charan, a consultant who works closely with GE's top management. "He raises the capacity of everyone he comes into contact with." Almost a full head taller than Welch (Immelt is six-four), and with a good deal more hair (London's Daily Telegraph called his "a luxuriant bouffant"), the former Dartmouth offensive tackle relies on what friends describe as a natural charisma, in contrast to Welch's sometimes assaultive style. "The guy doesn't use a tremendous amount of gun firing to get the job done," says Nicholas Heymann, an analyst at Prudential Securities. "He might put his hand on his revolver, but I've never seen him take it out of the holster." If the CEO were elected by employees, one insider says, Immelt would have won by a landslide.

Now he and his team want to prove they can win without Welch. "The fact is, GE has never been about one person," says Immelt, always quick to share credit. "The outside world is saying, 'We're not sure you can do it.' The inside world is saying, 'Just watch us.'" He adds: "I think longevity is a function of two things. It's a function of performance and your own ability to reinvent yourself. I think there will be zero honeymoon period for me, so performance has to be a given."

Analysts say earnings growth of 15% to 18% is all but "locked in" for two years. "You or I could run GE for a couple of years," argues Tichy. Even if Immelt stumbles early on, GE's patient approach could spare him the bum's rush; Welch has said it takes five years for a CEO to understand an organization. "Immelt will have a much longer runway than almost any other CEO," says James Citrin, an executive recruiter at Spencer Stuart.

Still, just meeting expectations--never mind exceeding them--will be a Herculean task. "It's going to be extremely difficult to meet the returns of the past ten years in the next ten years," says Bill Fiala, an analyst at Edward Jones. "Immelt would have to take the growth rate to levels that many people would argue are impossible." Just consider: If GE's stock rises over the next two decades as fast as it did over the past two, the company would end up with a market value of $19 trillion. That's roughly twice the U.S. gross domestic product.

Immelt insists that GE isn't close to hitting its limits. "We just don't believe in any of the rules of size," he said at a news conference. "I think what we've been able to prove is that the bigger we are, the faster we can grow." He deflects comparisons to Welch, saying, "I don't ever think about replacing Jack." And despite all the oversized expectations, GE's successor-in-waiting genuinely seems to be enjoying the ride. "I feel like I've died and gone to heaven," he says. "This is going to be a great run."

One hopes the run goes better than Phil Bengston's. The year he took over the Superbowl champion Packers, the team went 6-7-1. Bengston was gone after three seasons.

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