Apple Inc. (NASDAQ:AAPL) and Samsung have traded the title of world's biggest smartphone vendor over the years. That's a title that Nokia Corporation (ADR) (NYSE:NOK) once held but gave up in 2011 when Samsung overtook the Finnish vendor in Q3 2011 for the first time. Just one quarter later, Apple Inc. (NASDAQ:AAPL) became the king of the smartphone hill, driven by strong sales of the iPhone 4S. That didn't last long, as Samsung would reclaim the throne shortly thereafter.

Sammy pulls ahead This race has been a close call from quarter to quarter, but figures from both Strategy Analytics and IDC now show the South Korean conglomerate extending its lead. In the fourth quarter, both researchers estimate that Samsung sold approximately 63 million smartphones, earning a 29% market share. That's higher than the 47.8 million iPhones that Apple Inc. (NASDAQ:AAPL) sold to grab a 22% slice of the smartphone market.

Nokia is still working through its painful transition to Lumia devices; the 4.4 million Lumias it sold were two-thirds of the 6.6 million total smartphones it shipped during the fourth quarter. That puts the company's market share at 3%, down from the 12.5% it had a year prior. Nokia's making progress, though, as the company said demand outstripped supply of its newest Lumia 920, which was hurt by supply constraints.

Here's how the three companies finished out the full year.

Source: Strategy Analytics.

That's a big lead that Samsung has, selling almost 80 million more smartphones than Apple Inc. (NASDAQ:AAPL). Can Apple ever overcome Samsung's lead?

Where is this coming from? First, it's useful for investors to identify where Samsung is seeing strength. It's certainly not domestically in the U.S. market, since the iPhone represented 74% of total smartphone activations between AT&T Inc. (NYSE:T) and Verizon Communications Inc. (NYSE:VZ) combined. That means Samsung is enjoying success internationally and leveraging its massive scale, extensive distribution network, and large number of carrier partners.

On the high end, we also know that the iPhone still outsells Samsung's flagship Galaxy S model, which is now on its third generation. The company recently announced that the Galaxy S series has reached over 100 million units in channel shipments since the family was launched in 2010. The iPhone has sold over twice that during roughly the same time frame.

However, there's one high-end market where Samsung plays that Apple Inc (AAPL) hasn't touched yet: phablets. The 5.5-inch Galaxy Note 2 is off to a strong start and had reached over 5 million units in channel sales by November. Larger displays are growing in popularity but it's unclear if Apple will pursue this market segment.

We can also cross reference that data with these estimates. The Galaxy S III was launched in 2012, so substantially all 40 million of those units were shipped last year. The Galaxy S II debuted in April 2011, and Samsung said 10 million of those units shipped in the first five months. Depending on how many Galaxy S II units Samsung shipped in Q4 2011, that likely puts its 2012 shipments of that model between 20 million and 25 million.