Sometime in the next week or so, the zeros on the App Store countdown odometer will roll over and Apple (AAPL) will announce that 10 billion apps have been downloaded since the store opened two and a half years ago.

Asymco’s Horace Dediu has used the approaching milestone to run series of analytical charts. The first group, posted Sunday, showed that the number of apps downloaded per iOS device is accelerating and has grown from about 10 per iPhone and iPod touch in the fall of 2008 to more than 60 per iOS device today. Sometime later this year, the number of app downloads since 2008 will overtake the number of songs downloaded since 2003.

Of course, we pay for the music we buy from iTunes, while most of those apps are free. But there is money to be made supplying both kinds of content, and on Monday Dediu took a crack at estimating how much.

His conclusion: Apple has paid more than $2 billion to third-party app developers and about $12 billion to the music labels. To see his math, click here.

One more jackpot: Whoever downloads the 10 billionth app will win a nontransferable $10,000 iTunes gift certificate. Perhaps Mr. Dediu could calculate how many lifetimes it would take someone to spend all that.

[Follow Philip Elmer-DeWitt on Twitter @philiped]