Apple's market shares could double or even triple in the next few years, according to a new analysis.

In a note to investors on Wednesday, Sterne Agee's analyst Shaw Wu called Apple's growth the "ultimate platform adopting story."

Apple has "plenty of headroom for growth" in both the consumer and enterprise markets, according to Sterne Agee, which holds its compelling "buy" rating for Apple stocks, giving them a $500 price target.

 "As much success as AAPL has had, the company has only 4%-5% share in mobile phones and 4%-5% in PCs (12%-13% including the iPad)," noted Wu.

"We believe AAPL has opportunity to double or potentially even triple its market share in these end markets over the next few years, particularly with Greater China and international as underpenetrated opportunities."

In the next decade, there are three "secular mega trends" that will become the driving force, letting Apple to be the best-positioned tech company:

1) the mobile Internet, 2) cloud computing, and 3) the consumerization of technology.

Apple also has a compelling product release schedule toward the holiday season, including iOS 5, iCloud and a new iPhone on top of the recent release of OS X Lion and three new Macs (MacBook Air, MacBook Pro, Mac Mini), reports CNN.

The beauty of Apple's story, according to Wu, is "that the company doesn't need to win everyone over to continue success. The company just needs to continue winning a fair share of its vast end markets as more users get the AAPL advantage of 'it just works better."