Apple's (NASDAQ:AAPL) market share in China was bound to increase with the launch of its new iPhone models in the country. But the extent of the rebound in market share was less certain. As it turns out, the new models are doing extremely well in China, according to just-released data from Counterpoint Research -- better than the iPhone 5 did when it first launched, in fact.

Iphone

iPhone 5s. Source: Apple website.

Headed to the top?
By model, the iPhone 5s is already the top-selling phone globally, according to Counterpoint Research. That holds true in the important U.S. and Japan markets, too. In China, however, Apple is still lagging.

But here's the big news: Apple isn't doing so bad in China post-iPhone 5s and 5c launch. Counterpoint's data, which estimates sales (not shipments), shows Apple's market share of smartphones soaring from just 3% in September to a whopping 12% in October. That puts Apple in third place among smartphone manufacturers in China, up from sixth place in September. Even more, Samsung, with market share of about 18% of smartphone shipments in October, isn't too far ahead of Apple anymore.

China Mobile, too
Keep in mind, none of this data is yet affected by Apple's new arrangement with the world's largest carrier, China Mobile, to finally sell its iPhones on the network for the first time.

The imminent official announcement from China Mobile, rumored to take place on Dec. 18, comes simultaneously with the easing of supply constraints in Apple's supply chain. First reflected in full availability of the iPhone 5s in its retail stores in the U.S., channel improvement is also now evident in Apple's estimated shipping time of "Within 24 hours" for all capacities and colors for carrier-enabled versions of the iPhone 5s. Apple's always improving supply chain is perhaps poised to deliver record iPhones just in time for one of the most important carrier launches outside the United States.

With the help of China Mobile and easing supply, Counterpoint research believes that the irrefutably impressive demand for the new iPhone models could probably help Apple take the top spot in December or January -- ousting Samsung from its long held kingship over the China smartphone market.

It's an important market
Though Apple doesn't extrapolate China specifically in its operating data, it does provide data for Greater China, which includes China, Hong Kong, and Taiwan. In Apple's fourth quarter, this region accounted for 15% of Apple's revenue. If Apple continues its solid China iPhone sales in October through the rest of fiscal Q1, as Counterpoint Research projects, Apple's largest and most profitable product segment may send this small yet meaningful portion of Apple's total revenue soaring. Triple-digit sequential iPhone sales growth in the region for the quarter is beginning to look realistic.

Greater China growth would be welcomed warmly by Apple investors. In Q4, Greater China revenue was up just 6% from the year-ago quarter. Could soaring iPhone sales in China reignite Apple's Greater China growth rates?

Fool contributor Daniel Sparks owns shares of Apple. The Motley Fool recommends Apple and owns shares of Apple and China Mobile. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.