Apple is in third place among U.S. computer vendors with 10.6% of the market, according to the latest data from the Gartner research group (http://www.gartner.com). (And that’s not including the iPad, which Gartner doesn’t consider a computer, at least along the lines of a desktop and laptop.)

Apple’s market share grew 3.8% from the first quarter of 2011 to the first quarter of 2012, with sales going from 1,580,000 Q1 2011 to 1,640,814 in Q2 2012. Ahead of Apple in the U.S. were HP with 29% market share and Dell with 22.3%. HP experienced the strongest growth among the top five vendors in the U.S., as its shipments grew 6.6%, and its market share reached 29 percent in the quarter. Apple was the only other vendor among the top five to show growth in the quarter, as its shipments increased 3.8%.

Worldwide, the Mac still hasn’t cracked the top five. The leading computer vendors globally, as of Q1 2012, are HP (17.2% market share), Lenova (13.1%), Dell (11%), Acer (10.9) and Asus (6%).