As Hewlett-Packard Co. (NYSE: HPQ) and Dell have struggled as personal computer (PC) businesses besieged by the success of tablets and smartphones, China-based Lenovo has taken the spot as the world’s most successful PC maker. And it has a modest chance to be part of these faster growing tablet and smartphone sectors.

In Lenovo’s third quarter, revenue rose 15% over the same period a year ago to $10.8 billion, and net profit was up 30% to $265 million. Lenovo attributed much of its success to strides in tablets and smartphones, particularly in its home market of China. The company added that its plans to push quickly into emerging markets, which may be the last place left for rapid growth in PC adoption.

Lenovo claims it has more market share worldwide than any other manufacturer. IDC and Gartner have said as much in their widely regarded research. Based on the same sources, Lenovo’s share is rising faster than Dell’s or HP’s.

Lenovo management says the company’s share of the global market last quarter was 18.5%. Its fastest growth was in the relatively mature Americas region. This region is so saturated with PCs that Lenovo may be unable to hold its current growth rate, unless it can steal a much larger part of regional sales from its rivals.

Lenovo has started to break into the tablet and smartphone sectors, which have been dominated by Apple Inc. (NASDAQ: AAPL) and Samsung. It remains to be seen if it can continue this, particularly outside China. The company said tablet sales rose 326% over the same quarter of last year. However, the volume was tiny at 3.4 million units. Apple sold 26 million iPads in its most recently reported quarter. Despite a 47% growth of smartphone sales, only two million were sold outside China. Apple sold 51 million iPhones worldwide last quarter.

Lenovo management aggressively made the case that its buyout of Motorola from Google Inc. (NASDAQ: GOOG) would enhance its ability to take a large portion of the global smartphone market. Based on past failures of Motorola products, that forecast may well be wildly optimistic.

Lenovo’s annual revenue run rate has reached nearly $50 billion. At the center of that revenue, traditional PC and servers sales remain the dominate factors. But, compared to Dell and HP, it has at least a shot at the rapidly growing tablet and smartphone sector, which means it has a chance to succeed where its two rivals stumbled.

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