Apple Inc. (NASDAQ:AAPL) and Samsung Electronics Co., Ltd. (LON:BC94) are in a knock-down, drag-out fight. The moment one of them claws its way to the top, the other one reaches up and pulls it back down, grabbing the crown away. There are numerous market share reports conducted by various entities. Some show Samsung is the big leader, while others indicate just how important Apple Inc. (NASDAQ:AAPL) is to Americans.

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So who’s on top today? Canaccord Genuity issued a report today with an update on the smartphone market. There’s no question that Apple Inc. (NASDAQ:AAPL) and Samsung Electronics Co., Ltd. (LON:BC94) are still on top in the battle over smartphone market share.

During the fourth quarter of 2012, smartphone sales were strong, especially for LTE smartphones. The iPhone 5, Samsung Galaxy S III, Samsung Galaxy Note II and other LTE smartphones led the way during the fourth quarter. The analysts also found that the reduced iPhone 4 and 4S prices helped Apple Inc. (NASDAQ:AAPL) increase its smartphone market share from 15.4 percent in the September quarter to 21.7 percent in the December quarter.

However, they predict that when Samsung Electronics Co., Ltd. (LON:BC94) launches its Galaxy IV toward the end of March, they believe it will begin to pull away from Apple Inc. (NASDAQ:AAPL) once again, especially because they expect sales of the iPhone 5 to be much slower during the March quarter.

Canaccord Genuity also noticed during the fourth quarter of 2012 that the other smartphone companies (there are others?) have continued to struggle for market share. Research In Motion Ltd (NASDAQ:BBRY) (TSE:BB), Nokia Corporation (NYSE:NOK) (BIT:NOK1V) (HEL:NOK1V) and Motorola Mobility Holdings Inc (NYSE:MMI) all posted operating losses for the year.

The analysts’ January surveys showed “softer smartphone sales,” as expected after the holiday glut of smartphone purchases. Their surveys showed “solid sales” of both the iPhone 5 and the iPhone 4 at AT&T Inc. (NYSE:T), Verizon Communications Inc. (NYSE:VZ) and Sprint Nextel Corporation (NYSE:S). They also found strong sales for the Galaxy S III and Galaxy Note II “at all four leading U.S. carriers and in international markets.”