In a series of well-researched charts, Morgan Stanley’s Katy Huberty has put her finger on the one factor — all others being equal — that really drives smartphone sales: The number of cell phone operators that sell the thing.

In a report issued to clients Sunday, Huberty shared the results of an analysis of 760 carriers in 225 countries from 2007 to 2001. Over the past five years, the growth in total subscribers per year (17%) was split roughly 50/50 between new subscribers on existing carriers and subscribers signed up on new carriers.

This holds true in spades, Huberty suggests, for Apple’s (AAPL) iPhone, which since 2007 has gone from one carrier  — AT&T (T) — to nearly 230 carriers in 105 countries. (See chart above.)

Despite those carrier agreements, Apple still trails its competitors. Research in Motion (RIMM), for example, has deals for the BlackBerry with 79% of the 760 operators Huberty identified. Only 30% carry the iPhone.

The biggest opportunity for growth, according to Huberty (and, for that matter, Tim Cook) is in Asia, both in terms of total population and in terms of the number of subscribers who don’t have access to the iPhone because their cellular provider doesn’t sell it. See the charts below:

One last chart that also works in favor of cellphones, like the iPhone, with a relatively high sticker price: The growth in the number of subscribers in emerging markets who buy subsidized cellphones (in so-called post-paid plans) has recently overtaken those who prefer to pay full price for cheap cellphones at the time of purchase (so-called pre-paid phones).