Apple Inc is starting to hear a common refrain from investors: Show us the money.

After the death of chairman and chief innovator Steve Jobs last week, investors still like what they see at Apple: record demand for the latest iPhone 4S pushed its stock price near an all-time high. And it has a cash hoard of $75 billion.

A Thomson Reuters survey of 11 portfolio managers taken after the news of Jobs' death showed strong support for Apple's new management team led by Chief Executive Tim Cook, and confidence that Apple has at least a few years of great products in development.

But they also want Apple to start giving up some cash.

I would opt for a meaningful dividend, said Peter Deininger, a portfolio manager at Columbia Large Cap Growth Fund, one of Apple's largest investors.

Given the magnitude of the cash balance and the ongoing free cash flow generation, the company could make a statement about its ability to sustain those flows, Deininger added.

Six of the 11 money managers polled by Reuters called for a dividend payout as a reward for their loyalty -- something they fear will be tested as Cook tries to fill Jobs' shoes.

Ten portfolio managers said they still hold Apple stock on faith that Cook will be able to deliver on Jobs's vision in the near term. But five managers expect investor faith in Apple to be tested in the longer term.

I worry that Steve was a center of gravity for the company and, over time, people will say 'I wanted to work for Steve' and go and do something else, said David Eiswert of T. Rowe Price. That will be something to watch over the next year or two.

Apple has long resisted a dividend. It has put its money toward internal product development, made the rare acquisition -- and built its cash stockpile, which now accounts for about a fifth of its value. Apple's market cap soared to just shy of $349 billion when Jobs stepped down in August, from $5 billion when he returned to the company in 1997.

That unusual torrid growth in a large company has one money manager in the survey bracing for an eventual slowdown.

We haven't seen a company this size grow, so it has to decelerate, said Richard Sheiner of Geneva Advisors.

So far investors are sticking with the company.

The creative talent at Apple is broad and deep, and it has established a 'brand moat' with the consumer, said Nigel Holland, who helps manage $565 billion at Legal & General Investment Management.

And that's a big reason why three of the managers surveyed said they have bought up all the Apple shares they are allowed to.

There's every reason to own Apple stock, and we are committed to owning it over the next couple of years, said Keith Wirtz, chief investment officer of Fifth Third Asset Management.

Bruce Olson, co-portfolio manager of the Wells Fargo Advantage Growth Fund, agreed. The coast is pretty clear for them for the next five years, he said.

Beyond the short term, however, some shareholders are worried about whether Apple can continue to push out innovative gadgets after the product pipeline Jobs left behind is tapped out.

If we saw a slowdown on product launches and developments, that would give us some pause. Less people camping out for a few days to get the new product -- that would be symptomatic of it losing its touch, Wirtz said.

One fund manager polled is not waiting around for Apple to fall from grace.

We don't have shares in Apple, said Kim Caughey Forrest, vice president and senior analyst at Fort Pitt Capital Group. Jobs' death contributed to the skepticism, but it is also the closed environment of selling hardware and software together that works extremely well for consumers but not so well for business.

(Reporting by Edward Krudy, Sam Forgione and Supantha Mukherjee in New York; Editing by Edward Tobin and Matthew Lewis)