By Dan Mitchell
September 8, 2011

FORTUNE — It’s impossible to guess who might be Carol Bartz’s replacement at Yahoo because it’s impossible to guess what Yahoo might look like when a replacement is named. It could be a totally different company before a CEO is even chosen. Or choosing the replacement might be part of the transformation if, for example, the struggling Internet firm decides to sell itself.

Yahoo’s (YHOO) board complicates matters. Given its history — including its surprising choice of Carol Bartz in 2009 — it’s hard to know what it might do now. “I think HP and Yahoo are probably running neck and neck for the worst board in corporate America,” said Eric Jackson of Ironfire Capital in an interview with Bloomberg TV.

Jackson, like everyone else who is speculating on who might lead Yahoo, has former News Corp. (NWSA) executive Peter Chernin near the top of his list. Chernin, Jackson said, is “hungry” to “make his mark outside of Rupert Murdoch’s shadow.”

Chernin left News Corp. in 2009. He launched Chernin Group, a production and investment group that recently had success with the movie Rise of the Planet of the Apes. Chernin’s companies also produce TV shows and invest in media and technology firms in China and other Asian countries.

At News Corp., Chernin was the main force behind Fox Entertainment’s participation in Hulu, the video site that is owned by News. Corp., Disney (DIS), Comcast’s NBC Universal (CMCSA) and Providence Equity Partners. Hulu is selling itself, and Yahoo is among the bidders along with Microsoft (MSFT), Amazon (AMZN), AT&T (T), Google (GOOG) and others.

Even before Bartz’ ouster, Chernin was reported to be considering an acquisition of Yahoo as part of a group of investors. If he is indeed “hungry” to make his mark on the Internet under his own name, he might be persuaded to leave behind the Hollywood glamour.

Another possibility: Jason Kilar, the CEO of Hulu.  The former top Amazon executive is ad-savvy (something Yahoo desperately needs) and, obviously, knows a lot about Internet video. If Yahoo, which refers to itself as a digital media company, gets deeper into video, with or without Hulu, Kilar might be a good choice.

Jack Ma is CEO of China’s Alibaba Group, in which Yahoo has a 43% stake. He has battled with Bartz and would like that stake back — and maybe all of Yahoo. His company is worth far more than Yahoo is, so a stock deal is a possibility. Ma would then likely break off and sell pieces of Yahoo.

Yahoo’s board could decide to promote from within, though not without risk. In firing Bartz, the board named CFO Tim Morse as interim chief. It seems unlikely he’ll be installed permanently since he was hired by Bartz and, though he’s well-regarded as a cost-cutter, is also associated with Yahoo’s revenue slide. A clue to his prospects might be found in Kara Swisher’s description at AllThingsD of Morse’s presence at Yahoo’s “all-hands” meeting on Wednesday, where he was apparently nothing more than a supporting player to company co-founder and former CEO Jerry Yang. (Yang insisted that Yahoo is “not for sale,” but there’s little reason to believe him given the company’s distress.)

A more likely internal candidate is Ross Levinsohn, Yahoo’s executive vice president for the Americas. He’s in charge of Yahoo’s faltering display-ad business and its popular news, sports and finance properties — in other words, Yahoo’s most important businesses. Levinsohn came to Yahoo a year ago from Fuse Capital, an investment fund focused on digital media. As a News Corp. executive, he was in charge of that company’s acquisition of MySpace, which went on to become a spectacular failure.

A strong candidate is Jonathan Miller, News Corp.’s chief digital officer. He was CEO of AOL for four years until 2006. Miller won a gold star when he unloaded MySpace from News Corp. earlier this year. He was once a considered for the top Yahoo job, but was blocked by Time Warner, former owner of AOL, because of a noncompete clause. Given all the situation at News Corp., the timing perhaps could be august.

The timing probably couldn’t be worse for another potential candidate, though: Tim Armstrong, CEO of the beleaguered AOL (AOL). Not only is he struggling to make the disparate parts of his company work together, he’s also facing heavy criticism for his handling of the mess surrounding Michael Arrington and TechCrunch. Still, if Yahoo and AOL were to partner in some way, Armstrong could come out on top.

Yahoo has to endure some major changes no matter what, but nobody seems to know what they should be. It could be acquired, or it could sell off major chunks of itself — perhaps its Asian businesses including Alibaba and Yahoo Japan — and use the cash to make acquisitions of its own. For years, people have been asking: “What is Yahoo?” Any new leader has to be able to answer that question in a single, concrete, believable phrase.

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