The institutions that hold 70% of Apple’s (AAPL) shares lobbied Steve Jobs for years to put some of his company’s rapidly growing cash hoard in their hands.

Now that his successor is talking openly about the company’s discussions to do just that, the sell-side analysts have started to calculate how big their share might be.

The latest to weigh in is Morgan Stanley’s Katy Huberty, who pointed out in a note to clients Wednesday that in addition to the $34 billion in cash and marketable securities Apple has in the U.S. and the $64 billion it holds overseas, it will generate at least $18 billion in free cash flow this year in the U.S. alone.

If the company distributes 50% to 100% of that cash to shareholders, that works out (at a $500 share price) to a 1.9% to 3.8% dividend. This is important, says Huberty, for three reasons:

• Apple can support a dividend with above-market yield using only US free cash flow… This range compares favorably to the S&P 500 average yield of 2.2% and IT sector average of 1.2% in 2011
• A dividend could boost long-term stock performance. Since 2002 (post the tech bubble), the top one-third of tech stocks ranked by dividend yield have outperformed the bottom third by 14%
• In the near-term, investors are also showing a preference for dividends. Tech dividend payers’ traded at a P/E multiple that represented a 28% premium vs. non-payers last year.

Given the new products (iPad, iPhone, etc.) coming online, Huberty believes the prospect of a dividend could drive Apple’s share price past her current target of $515 to her “bull case” of $600 per share.