The United States advertising industry is one constituency hoping that Yahoo remains independent and intact. It often looks at Google and Microsoft as competitive threats that increasingly seek to broker the sale of ads in all media formats and even in some cases to help advertisers create their own Internet spots.

There is a new parlor game in Silicon Valley: guessing who will replace Jerry Yang at the helm of the troubled Internet giant Yahoo.

Yang, a Yahoo co-founder, said Monday that he would relinquish the chief executive role once a successor is named and revert to being "chief Yahoo," the strategy position he held before his 18 turbulent months of running the company.

But even before a new boss is selected, Yahoo has an even more fundamental decision to make, analysts and other Internet watchers say. Does it want to remain an independent company, trying to grow in a range of businesses while it fights Google in the crucial arena of Web search? Or should it finally listen to the devotees of deal-making and sell some or all of itself to another Internet player, most likely Microsoft?

Yahoo shareholders are clearly rooting for a deal. Shares of Yahoo rose 8.7 percent, or 92 cents, Tuesday to $11.55, largely on hopes that Yang's departure might help push the company into the arms of an acquirer.

Steven Ballmer, Microsoft's chief executive, has said he has no interest in making another bid for Yahoo, but he has expressed repeated interest in buying Yahoo's search business. Many observers and Internet veterans agree that this remains the company's most attractive option.

"Yahoo is still in many ways the definitive brand of the consumer Internet, but I don't think they can or should compete with Google any longer," said Ross Levinsohn, a former president of Fox Interactive Media. "That game is over."

If the Yahoo board agrees, it will want an experienced chief executive with a history of deal-making who is also capable of running the online media properties left behind.

Potential candidates who could embrace this vision of Yahoo include Peter Chernin, the president of the News Corp.; Jonathan Miller, a former chief executive of AOL; and John Chapple, president of Hawkeye Investments, who was listed on the alternative slate of Yahoo directors offered by Carl Icahn, the activist investor, during a proxy battle last summer.

But some observers think Yahoo's board could forgo any kind of deal with Microsoft and select a leader who stabilizes the company, unifies its employees and tries to capitalize on its broad technological assets. Potential candidates that fit with this strategy have strong technical backgrounds and include Marc Andreessen, the co-founder of Netscape, and Jeff Jordan, a former eBay executive who runs the online reservations start-up OpenTable.

Susan Decker, the president of Yahoo, will also be considered for the job, although analysts say anyone from Yahoo's current leadership would encounter significant skepticism from investors.

The U.S. advertising industry is one constituency hoping that Yahoo remains independent and intact. It often looks at Google and Microsoft as competitive threats that increasingly seek to broker the sale of ads in all media formats and even in some cases to help advertisers create their own Internet spots.

Yahoo, on the other hand, remains a largely unthreatening friend.

"The ad community doesn't want another big Internet player sitting in the hands of someone that competes with them," said Mike Leo, the chief executive of Operative, a digital advertising technology firm.

To avoid deals that would break up Yahoo, a new chief executive would need to tackle some of the well-chronicled cultural problems that former employees said seemed to get worse under Yang.

These include a climate of indecision, constant, interminable meetings and widespread overlapping of responsibilities. The new chief executive will also have to deal with a legacy of head-scratching management moves -- like Yahoo's announcement last month that it would lay off 10 percent of the company but would not announce who was being cut until December. That put Yahoo employees under a two-month cloud of uncertainty.

Whatever the Yahoo board decides to do, it still has considerable assets with which to work. The company still attracts 500 million users a month, is the leading Web e-mail service and has many other profitable Internet franchises in news, sports and video.

It also remains one of the top brands on the Internet, even if the exclamation point at the end of its name now looks wildly overexuberant.

"This isn't like AOL. They actually have a big loyal audience that isn't going away," said David Card, an analyst at Forrester. "They just need to pick their battles more sensibly."