Source: Morgan Stanley

One of the biggest drivers of Apple’s AAPL growth — and the company’s share price — over the next two years will be the expiration of the exclusivity deals Steve Jobs cut with carriers during the iPhone’s first two years.

That’s the conclusion of a surprisingly bullish report issued Friday by Morgan Stanley’s Kathryn Huberty, long considered a leading Apple bear.

“We expect Apple to broaden iPhone carrier distribution over the next two years and believe this opportunity is under-appreciated by the investment community,” she wrote. “This total opportunity is substantial — it adds up to an incremental 20.3M iPhone units and $3.76 in adjusted EPS, 100% and 41% of iPhone units and adjusted EPS respectively.”

Her “case study” is France, where the iPhone’s market share grew 136% after the government ended Apple’s exclusive deal with Orange. She expects similar — if not quite as dramatic — increases as Apple, in addition to opening new markets in China and Korea, switches to multi-carrier agreements in its largest markets. (The U.K. has already gone multi-carrier.)

The U.S. is the biggest prize in this respect, but she doesn’t expect Apple to cut a deal with Verizon before that carrier’s so-called 4G rollout is complete, some time in 2011.

Huberty offers three scenarios for investors — bullish, base and bearish — represented in the chart above. Using her base scenario she expects Apple to sell 41.7 million iPhones in calendar year 2010. She has raised her revenue estimate for 2010 to $45.3 billion from $38.2 billion and her estimated EPS to $10.50 — 13% above the Street’s consensus.