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.

See also:

• The iPhone casts a giant shadow on the Web
• iPhone now represents 51% of U.S. smartphone traffic – report