Apple Inc.’s (NASDAQ: AAPL) share of the Chinese smartphone market rose to 12% in October, according to technology market research firm Counterpoint. That was a leap from its 3% share in September and made it the third-largest smartphone player in the People’s Republic, overtaking Huawei and ZTE but still trailing Samsung and Lenovo.

This leap in market share comes ahead of the anticipated roll-out of iPhones on the China Mobile Ltd. (NYSE: CHL) network, which could come as soon as early 2014. China Mobile is the world’s largest cellphone carrier, with more than 700 million subscribers. Counterpoint expects Chinese sales of the iPhone 5s to be boosted even further, with Apple perhaps being the top smartphone player in China by December or January. The firm even predicted a price war after China Mobile begins to carry iPhones as it tries to fend off its rivals.

But others disagree about how much of a boost Apple will see in iPhone sales after the roll-out. Merrill Lynch analysts see fewer than 10 million units incremental added in sales. But R.W. Baird projects that Apple could sell 12.5 million to 30 million iPhones to new customers. We wondered how many Chinese customers could even afford a new iPhone.

Apple’s iPhone 5s continued to be the bestselling phone globally in October, followed by the iPhone 5 and then Samsung’s Galaxy S4. Sales of the Galaxy S4 have been slipping, though Samsung’s Note III rose to the number five spot on Counterpoint’s list for October.

comScore recently reported that Apple’s share of the U.S. smartphone market only grew by 0.2% to 40.6% in the three months that ended in October. Samsung’s share grew faster, by 1.3%, to 25.4% in the same period, as the lower priced phones from Samsung attracted more new smartphone subscribers while the relatively higher priced Apple models replaced older iPhones.

In the ongoing battle between Apple and Samsung on the patent front, Samsung lost another round Thursday after a Korean court ruled against it in a dispute related to messaging technology used on mobile devices. Samsung had claimed that Apple’s iPhone 4s and 5s models had violated two of its patents.

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