See the blue slice in the pie chart at right? It represents the iPhone’s share of U.S. smartphone traffic on the network maintained by AdMob, one of the companies that run those little ads that appear on the screen of your mobile phone.

We’ve been watching that slice grow over the past few months. In February it covered 51% of the pie. By April it had grown to 59%. And by Thursday morning, when AdMob released the May edition of its U.S. smartphone pie, Apple’s AAPL share had grown to 69% — a 10 point increase in one month.

Some caveats are in order. This is just one company’s view of the mobile Web — albeit the view of world’s largest supplier of mobile ads, serving 6.3 billion banner and text ads per month. And it’s only a snapshot of the smartphones on the U.S. portion of the AdMob network — although 47.6% of AdMob’s traffic comes from the U.S. and 37.3% of that comes from smartphones.

Still, what it suggests is that Apple’s domination of the smartphone market — the only part of the cellphone market that has continued to grow in the face of the recession, according to Gartner Research — is accelerating.

How tough this makes it for the competition is even clearer when you look at AdMob’s report on the total U.S. handset market — one that includes smartphones, so-called feature phones and devices that aren’t phones at all, like the iPod touch. Apple’s share of this market, viewed through AdMob requests, is 45.1%, having grown 10.4% between April and May. Most of the other players in the field — including Research in Motion RIMM , Samsung, Motorola MOT and Palm PALM — are showing negative growth. We’ll be watching next month to see if Palm’s share grows once AdMob starts to get data from the Pre.

Below the fold: AdMob’s worldwide data, in which Apple’s share  (31.4%) and share change (5.2%) are smaller, but the pattern is basically the same. You can see the full report here.

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