PALO ALTO, Calif. (CNN/Money) - Riddle me this: What do you get when a giant credit-card company masquerading as a retailer sheds its credit-card operations?

The answer, of course, is Sears, Roebuck & Co., the venerable company that used to call itself the World's Largest Store and whose softer side of late has been the sales and profits from selling clothes and appliances.

The more important part of the business -- about two thirds of operating earnings -- comes from its various credit-card operations, long a mixed blessing for Sears.

The credit-unit blessing is mixed because on the one hand, obviously, it generates profits. On the other hand, concerns about the business (bad debt, delinquencies, etc...) have been a constant worry for Sears (S: Research, Estimates) and its investors as well as a distraction to management.

To rectify the situation, on Tuesday Sears took out the cheapest, most powerful ad it could find in order to put its credit-card operation on the block -- it leaked word to major newspapers that it had retained Goldman Sachs to sell the unit.

Though Sears CEO Alan Lacy declined to comment Wednesday in a conference call with analysts on what he thinks the credit operation is worth, his bankers whispered to reporters that it should fetch as much as $7 billion.

That's an interesting figure, considering that before Wednesday's 13 percent increase in the value of Sears shares, the entire company was worth about $6.8 billion.

The company speaks of "unlocking" the value of its retailing unit by jettisoning the credit-card operation. But what if the key opened the door that revealed a retailer that truly isn't worth anything?

I commented here late last year on the myriad stocks a buy-and-hold owner of AT&T from the early 1980s would have today.

Now I think I've found a company that's aiming to be a worthy competitor in the spin-off race: the various remnants of the old Rockwell International.

Recently by Adam Lashinsky NYSE: Who's minding the store? Take your profits We win, then what?

Had you bought shares of Rockwell in the mid-1990s and never entered a sell order, today you'd own -- by my count -- shares of five companies, with the list growing rapidly.

Milwaukee-based Rockwell Automation (ROK: Research, Estimates), technically is the survivor to the former Rockwell International, which sold its rocket-technology business to Boeing in 1996.

Rockwell Collins (COL: Research, Estimates), used to be Rockwell's avionics division and is in Cedar Rapids, Iowa.

Troy, Mich.-based ArvinMeritor (ARM: Research, Estimates), is partly Rockwell's former automotive parts business.

And Conexant (CNXT: Research, Estimates), Rockwell's one-time semiconductor unit, is doing its share first by having spun off a chip company in Woburn, Mass., called Skyworks Solutions (SWKS: Research, Estimates), and, soon, its Internet gear unit, Mindspeed Technologies, a deal announced Tuesday.

And there could be more. Last year Conexant "contributed" its wafer fabrication facility to a venture with the Carlyle Group (of defense industry and Mideast connections fame) called Jazz Semiconductor. Should that enterprise be successful it wouldn't be a surprise to see it spun off to Conexant shareholders.

Imagine the banking fees.

Adam Lashinsky is a senior writer for Fortune magazine. Send e-mail to Adam at lashinskysbottomline@yahoo.com.

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