Updated from 3:34 p.m. EST

Wall Street analysts gave investors in Apple ( AAPL) an early Christmas present on Monday: a bundle of upbeat reports that helped send the company's shares to an all-time high.

Apple's iPod digital music players appear to be a holiday hit, selling out or in short supply at a number of retailers, the analysts noted. That, plus the potential for an even better year next year, led analysts at Deutsche Bank and Piper Jaffray to raise their price targets on Apple's stock.

"Our checks over the Thanksgiving weekend suggest that demand for iPods and iMacs is strong and that Apple has sufficient supply to meet demand (so far)," said Deutsche Bank's Chris Whitmore, who raised his price target on Apple to $79 from $60. "We believe Apple is off to a very strong start to the holiday season."

Apple has been a non-investment-banking client of Deutsche Bank in the last 15 months.

With the help of such sentiments, Apple's stock edged upward to as high as $71.07 -- a new high -- in intraday trading on Monday. At the close, the company's shares were up 32 cents, or less than 1%, to $69.66.

Investors have been particularly bullish on Apple in the last six months. While the company's shares have more than doubled in the year to date, they are up 94% just since mid-June.

And many on Wall Street expect the bull run to continue.

The company's revival began with its launch of the popular iPod four years ago. Sales of the devices now comprise about one-third of Apple's total revenue, and for years this has been the fastest-growing part of its business. If the analysts' reports are correct, the company's digital music players are as in as high demand as ever this holiday season.

While Apple's own stores appear to have ample supplies of iPods, third-party retailers such as Circuit City ( CC), Best Buy ( BBY), CompUSA, Target ( TGT) and Amazon.com ( AMZN) appear to be running low, the analysts reported, with individual stores either sold out of particular iPod models or -- in the case of online stores -- reporting long wait times before the devices will be shipped.

But the low availability doesn't appear to be discouraging shoppers. On Amazon, for instance, various iPod models dominated the company's lists of best-selling products in the digital music player and overall electronics categories, analysts noted.

Noting this demand, Whitmore raised his estimate on the number of iPods that Apple will sell this quarter from 9.5 million to 11 million. In particular, he predicted that the company would sell more of its high-end video iPods than previously expected; that should help boost the company's bottom line. Including stock options costs, Whitmore now expects Apple to earn 54 cents a share in its first quarter, up from a previous estimate of 49 cents a share.

Other analysts were bullish on Apple's iPod sales but were more concerned about whether the company might leave sales on the table this quarter. J.P. Morgan's Bill Shope, for instance, predicted that Apple would sell more than the 10.8 million iPods that he previously forecast this holiday season. But he noted that Apple's retail partners were sold out of iPods on the Friday after Thanksgiving.

"We expect Apple to continue to aggressively replenish channel inventories throughout December, but demand is likely to continue to exceed supply," said Shope, whose firm has provided non-investment-banking business for Apple in the last year.

And some analysts were even more concerned. Piper Jaffray's Gene Munster, for instance, argued that the Street might be getting ahead of itself on iPod sales. Instead of being a bullish sign, the fact that iPods are sold out at places such as Best Buy is an indicator that Apple is not going to be able to meet demand, he said. Unlike his peers, Munster decided to stand pat with his forecast of 9 million iPods shipped, though he added that Apple might narrowly exceed that number.

"We continue to believe that some Street estimates for iPod unit shipments for the December quarter are too high," said Munster, whose firm has not recently done investment banking for Apple. "We do not expect Apple will be able to ship the number of units that are already anticipated in some Street models."

Still, Munster found other reasons to be bullish on Apple. Demand should remain strong for both iPod products and the company's Macintosh computers, he said. Indeed, Apple's upcoming switch to processors made by Intel ( INTC) should spur a wide range of updates to the company's computer lineup, he said. In the past, such updates have led to increased sales.

Munster, too, raised his price target on Apple, going to $79 a share from $68. At that higher price, Apple's valuation would be 45 times its expected earnings over the next year, which is in line with its three-year average, he said.

"Apple's domination in digital music is a critical piece to the story, but we do not believe iPod is the only growth avenue for the company. Indirectly, we expect iPod to continue to be a foundation for growth in other parts of Apple's business," Munster said.