Yahoo shares opened up 7 percent Wednesday following the ouster of CEO Carol Bartz, perhaps on speculation the rudderless Internet search engine might be a target.

Sunnyvale, Calif. -based Yahoo, probably one of the world's best-known brands, has great value. Its market capitalization exceeds $17.3 billion and its enterprise value is $13.8 billion. Any bidder would look at the latter figure first.

That's a big bite for any company at a time when there are fears of recession worldwide. But Yahoo remains one of the top search sites, with 3.3 billion daily queries in June alone, according to comScore data.

While Yahoo searches fell 13 percent, Google's dropped 1 percent. While Google accounted for about 63 percent of all core searches, comScore reported, Yahoo was No. 2 with nearly 18 percent.

Clearly, one company that couldn't dream of acquiring Yahoo is Google, which is being probed for possible anti-competitive practices by the U.S. Federal Trade Commission as well as the European Commission.

Another unlikely bidder is Microsoft, which once bid for Yahoo and already handles part of its search engine under a deal negotiated by Bartz. But Microsoft has just come out of a federal judge's supervision of its antitrust consent decree.

More likely prospects could include Japan's SoftBank, which was an original Yahoo investor. CEO Masayoshi Son, a Korean Japanese, is a billionaire in his own right. SoftBank owns major stakes in Yahoo Japan, where the company is very strong, as well as in China's Alibaba and Renren, the social networking site.

Traditional media companies that are moving into digital advertising and for-pay models might also look. One prospect could be Rupert Murdoch's News Corp., which has been successful attracting paid subscribers to its site for the Wall Street Journal. But News' prior foray into Silicon Valley, MySpace, was a financial bomb.

Others who might take a look include Washington Post and AOL, although their respective market capitalizations are too small. Neither exceeds $2.7 billion.

Several technology companies have gone private, such as Freescale Semiconductor, Seagate Technology, SunGard and others in multi-billion dollar deals. That would be the price for Yahoo, where the board would also insist on some kind of premium for the brand name.

There are a number of companies that played in this game before in private equity. One is Silver Lake Partners, which twice acquired Seagate and twice helped bring it back in IPOs.

Another is Providence Equity Partners, where former TimeWarner CEO Richard Parsons is now a senior adviser. Providence specializes in technology and media and invested in Univision, SRA International and CDW, the computer services provider.

But a buyout would require partners, financing and the willingness of Yahoo's future CEO and board to take on debt, which might not be paid off quickly if Yahoo can't attract eyeballs and advertisers.

Other private equity players that might join in could include TPG Capital, Blackstone Group, Carlyle Group and Europe's Permira Advisers which bought Freescale and helped take it public again this year.

Another famed private equity firm Kohlberg Kravis Roberts, might also be interested, although its record in technology is mixed. It became a strategic investor in Sun Microsystems before the company's takeover by Oracle and maintains a similar investment in Eastman Kodak, which is auctioning patents.

KKR joined with other PE companies including  Bain Capital, once led by Republican presidential candidate Mitt Romney; England's Apax Partners and Dutch Alpinvest Partners to buy NXP, the semiconductor division of Philips Electronics, for $9.4 billion.

If Yahoo were to go private, a syndicate of some of these top players, perhaps joined by a Chinese investor like Alibaba or Renren, might write the next chapter of Yahoo's 17-year history.