Touchscreen phones are on fire, comScore reports, and Apple is leading the pack. For now.

Three months ending Aug. 2009. Source: comScore MobiLens

There’s a thundering herd of imitators behind it, but Apple’s AAPL iPhone still dominates that fastest-growing segment of the U.S. smartphone market, according to a comScore report issued Tuesday.

Touchscreen mobile phone adoption in the U.S. grew at a breakneck 159% rate last year, comScore reports, easily outpacing the 63% growth of the broader smartphone market.

By last August, nearly 34 million Americans were carrying smartphones, 23.8 million of them touchscreen devices. And of those touchscreen phones, 32.9% were iPhones.

“The iPhone clearly set the trend in the industry for touchscreen devices, so it’s no surprise that it has the largest share of the market,” said comScore VP Mark Donovan. “But as other players have entered the touchscreen market with compelling devices, competition is clearly heating up.”

Donovan mentioned Google’s GOOG Android platform in particular, although the closest Android contender in August was the T-Mobile DT G1 running a distant seventh after two proprietary LG phones, the BlackBerry RIMM Storm, the Palm PALM Pre and the Samsung Instinct.

Below the fold, comScore’s spreadsheets, including one that shows preference by age group. (The smartphone sweet spot seems to be ages 24 to 34.)