Apple shipped over 13.5 million mobile computers in the second quarter of 2011 (Q2’11) for 136% year-over-year shipment growth, overtaking HP for the top spot, according to preliminary results from the latest DisplaySearch data (http://www.displaysearch.com).

Nearly 80% of Apple’s mobile computer shipments were iPads, which reached over 10.7 million units, for 107% year-over-year growth. Apple’s total mobile computer shipments (notebook and tablets) were 3.9 million units more than HP’s nearly 9.7 million units for the quarter.

From a category perspective, tablets continue to be the engine of growth for the mobile computer industry, notes DisplaySearch. Tablet shipments were up nearly 70% quarter-over-quarter and over 400% year-over-year with nearly 16.4 million units shipped in Q2’11.

Notebook shipments were down 2% quarter-over-quarter but up 2% year-over-year with nearly 48 million units shipped in Q2’11. A consumer notebook adoption slowdown continues to hold back the industry following a 2% year-over-year drop in shipments in Q1’11. Worldwide mobile computer shipments (including notebook and tablet PCs) reached 64.4 million in Q2’11, up 10% quarter-over-quarter and 28% year-over-year, notes DisplaySearch.

Among the top five players, Acer experienced the largest decline in shipment growth. Acer’s shipment growth declined in Q2’11, falling 4% quarter-over-quarter and 12% year-over-year.

In the notebook category, Samsung and Dell had the fastest shipment growth, up 44% and 33% year-over-year, respectively. Dell was also up quarter-over-quarter with 27% shipment growth. Samsung’s shipments fell 16% quater-over-quarter as it was unable to build off of strong shipment results in EMEA and China. Still Samsung was able to top Q1’11 shipment levels in North America and Asia Pacific.

Tablet shipment results show that even after removing Apple from growth rate calculations, worldwide year-over-year tablet shipment growth reached 25%, and shipments of non-Apple tablets reached over 5.6 million units for the quarter, says DisplaySearch.