I suspect that the number one question on the mind of Apple (AAPL) shareholders gathering today at 1 Infinite Loop for the company’s annual meeting is what Tim Cook plans to do with Apple’s roughly $100 billion in cash and marketable securities.

“I think it’s clear to everyone, and I’d be the first to admit, we have more cash than we need to run the business on a daily basis,” Cook told investors at a Goldman Sachs conference last week.

What will he do with all that extra dough? Speculation (see, for example, here) has centered on four scenarios:

• Pay an annual dividend. Morgan Stanley recently calculated that Apple could pay 1.9%-3.8% out of U.S. cash flow alone.
• Start a share repurchase plan. $100 billion at Apple’s current price could retire more than 190 million shares.
• Announce a stock split. Apple hasn’t had one of those since the 2:1 split it announced in February 2005, when it was trading for less than $90 a share. It closed Wednesday at over $513.
• Pay a one-time dividend: Apple could afford to shell out as much as $25 per share without touching its overseas holdings.

Judging from Cook’s remarks last week, however, I’d say the most likely scenario is none of the above — at least for now.

While repeating previous remarks about not being “religious” about holding on to extra cash and being engaged in “active discussions” about what to do with it, Cook went on to say: (I quote)

• We spend our money like it’s our last penny. I think shareholders want us to do that. They don’t want us to act like we’re rich, and we’ve never felt that way honestly.
• I think everyone would want us to be deliberate and really think through, and that’s what we’re doing. We’re not going to go have a toga party or do something outlandish, and so people don’t have to worry [the cash] is going to burn a hole in our pocket.
• I only ask for a bit of patience, so that we can do this in a very deliberate way and make the best decision for the shareholders. (transcript)

Finally — and this may be the clincher — Cook said “we’re in very active discussions at the board level on what we should do.” A close reading of Apple’s 2012 proxy  suggests that while the three-person audit committee met nine times in 2011, there may have been only one full board meeting (last November) since Aug. 24, 2011, when Steve Jobs submitted his resignation.

It’s hard to imagine a multi-billion dollar decision like this being made without at least one more meeting of the full board.

UPDATE: Meeting over. No dividend or buyback or stock split today. See here.

The shareholders meeting is scheduled to begin at 10 a.m. PT (1 p.m. ET).