After a string of disappointing quarters, Hewlett-Packard CEO Léo Apotheker killed the Palm hardware unit and proposed spinning off personal computing to focus the company on enterprise software. Now HP’s board looks set to kill Apotheker’s tenure to focus the company on finding new leadership.

Early reports that HP’s board was meeting to oust Apotheker and potentially replace him with ex-eBay head (and California gubernatorial candidate) Meg Whitman began filtering out through press leaks yesterday morning. The New York Times had the fullest account of the board’s reported deliberations, citing unnamed insiders “not authorized by the board to speak publicly.”

Still, it wasn’t clear what exactly was happening; industry sources I spoke to who’d heard some of the earliest reports were equally inclined to see it as a trial baloon, an attempt by unhappy forces within HP to force the board’s hand, or even some kind of complicated ruse to flush out bids for HP’s personal computing division. (If you want to hear some stone realpolitik Kremlinology, talk to people in the business-facing software business. Those people don’t play.)

Now, though, Apotheker’s ouster at least seems quite likely. The Times‘ James B Stewart published a story treating the firing as practically a fait accompli, with on-the-record sources giving accounts of a deeply dysfunctional board ambivalent about hiring Apotheker in the first place. Even if the Whitman trial balloon rumors turn out not to be true — and most of the credible sources willing to dish about everything take pains to emphasize that discussions about Whitman are early, she may not be hired, and she isn’t exactly a perfect fit — it seems like the board is serious about making another major change, and that Apotheker is in trouble.

This partially explains some of the strange HP news items that have filtered out since Apotheker’s controversial move to scuttle HP’s TouchPad tablet and the Palm/webOS smartphone and hardware division. Three weeks ago, we wrote that HP/Palm seemed to be actually be adding webOS engineers and managers; this week, reports emerged that nearly the entire webOS team would be sacked through massive layoffs.

When you run a company as large and varied as HP, you effectively manage a team of junior CEOs who each are charged with giant companies. All of them have a stake in preserving their own units and reputations; big shake-ups of the kind Apotheker proposed, coupled with his brief tenure and relative lack of allies within HP, were bound to lead to a large number of very powerful and deeply unhappy people.

Add tanking stock, an inability to attract buyers for the PC division, increasing outflows to customers and vendors over the TouchPad debacle, and what seemed to many like an overenthusiastic acquisition price for British business software company Autonomy, soon both large and rank-and-file investors were profoundly displeased, too. Some even sued, claiming the company’s executives misled investors about how badly it was stumbling.

The HP board may not make a decision on Apotheker until as late as Friday, AllThingsD’s Kara Swisher reports. An interim CEO may simply carry out the planned personal computing group spinoff and try to keep the company afloat until it decides who would best lead the company going forward. Whatever “forward” might turn out to mean.

If HP does move to hire a new permanent CEO, all bets are off. Apotheker’s reign shows that when a new CEO tries to carry out the business vision of the outgoing chief, the company will lose its way.

Refocusing the company on enterprise and cloud may still make sense as a strategy, but the particulars of how, when or even whether that will happen can’t be treated as certain any more.

So even if Apotheker’s ouster will satisfy those calling for someone to be held accountabile for this mess, HP will likely be chaotic for quite some time.