The business of selling ads on smartphones and other handheld devices is growing like gangbusters, but tracking it got a bit trickier after two of the biggest mobile ad networks were swallowed up — AdMob by Google (GOOG) and Quattro Wireless by Apple (AAPL).

But the third, Millennial Media, is still independent and still churning out monthly snapshots of how the various device manufacturers divide up what has grown into a billion-dollar pie.

At right, we’ve copied the latest report, for July, issued Wednesday morning, as well as June’s, so you can see how market shares are shifting. Apple, which has had the No. 1 spot since September 2009, still gets the lion’s share of mobile ad requests. Google’s Android moved into the No. 2 spot in July, overtaking Research in Motion (RIMM). Non-phone connected devices (iPads, iPod touches etc.) also gained significant share.

But these pie charts are misleading because they don’t show how the overall market is growing. For example, although Apple’s iOS lost a percentage point of market share in July (from 56% to 55%), its ad requests were actually up 24% month over month. Below: the growth figures on Millennial Media’s ad network as provided by Wednesday’s report.

• Android ad requests grew 47% month-over-month. Since January, Android has grown 690%.
• iOS ad requests increased 24% month-over-month. Since January, iOS has increased 15%.
• RIM ad requests increased 18% month-over-month. Since January, RIM has increased 66%.
• iPad ad requests grew 327% month-over-month.

Millennial calls itself the leading independent mobile ad network. According to Nielsen, it does have the largest reach in terms of U.S. audience size, with access to 63 million of a total of 77 million mobile web users, or 81% of the U.S. mobile Web. You can read their full report here.

[Follow Philip Elmer-DeWitt on Twitter @philiped]