According to the latest results from the Gartner research group, Apple has 8% of the US computer market for the first quarter of 2010. That’s up 34% from the 7.2% of the same period a year ago.

That places Apple fifth among US computer vendors. Ahead of it, with first quarter 2010 market share percentages, are HP (25%), Dell (23.4%), Acer (15.6%) and Toshiba (8.6%). Worldwide, Apple still doesn’t rank in the top five, which are: HP (18.2%), Acer (14.2%), Dell (12.1%), ASUS (5.5%) and Toshiba (5.5%). The Mac has, by most estimates, a 5% global market share.

Worldwide computer shipments totaled 84.3 million units in the first quarter of 2010, a 27.4% increase from the first quarter of 2009, according to preliminary results by Gartner. These first quarter results have exceeded Gartner’s earlier market outlook. Gartner had been expecting first quarter computer shipments to grow 22%.