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Apple is catching up to Research In Motion in a smartphone market that saw 54.7 million units ship in the first quarter of 2010, up 56.7 percent from the first quarter of 2009.

Nokia commanded the lion’s share of the burgeoning market, shipping 21.5 million units for the quarter to take 39.3 percent of the worldwide market, according to research company IDC.

RIM shipped 10.6 million BlackBerry smartphones in the first quarter, giving it 19.5 percent of the burgeoning market for handheld devices with full HTML Web browsers.