New numbers show Android-based tablets are gaining on the reigning champ, Apple’s iPad. Although Android owns 39 percent of the tablet market, some question whether there’s a ringer: Amazon’s Kindle Fire. The device is the first non-Apple tablet to lay a hand on the iPad, but uses a highly-customized version of Google’s mobile operating system. How much of Android’s gains are due to its barely-recognizable distant cousin, twice removed?

According to Strategy Analytics, which released the numbers this morning, Android tablets captured a record 39 percent of the market in the fourth quarter of 2011. That’s up from 29 percent over the same period in 2010 – a 10 percent jump. Meanwhile, Apple’s lead has been shaved to 57.6 percent, down from 68.2 percent in 2010. Microsoft is just getting on the scoreboard, registering 1.5 percent of the tablet market, an increase from goose egg in 2010.

The researchers lumped the Kindle Fire in with other Android tablets, although the version of Google’s software powering the Amazon device would not be mistaken for the heart of a Samsung or Motorola tablet. The Kindle Fire’s Android is optimized for Amazon’s services, such as e-books, cloud storage and simple video. That sort of customization helped the Kindle Fire become the No. 2 tablet, the first to make Apple even breath a bit heavier. It’s questionable whether Android tablets would see a 10-point jump in market share without help from the Kindle Fire.

The one factor in the Strategy Analytics report: it’s numbers are based on actual sell-through rather than simple shipments. The difference is that sell-through counts the number of products that reach customers’ hands, rather than what’s unloaded onto the shelves of your local electronics retailer.