Microsoft CEO Steve Ballmer said that the company expects its hardware partners to ship 350 million copies of Windows 7 this year, outpacing sales of the OS in previous years. But this year’s sales estimate is particularly impressive because Microsoft is planning to ship Windows 7’s successor, Windows 8, sometime in the fourth quarter.

“Windows is the single most popular system,” Ballmer said this week at a Seoul, Korea, tech conference, drawing the same comparison with newly competitive smartphone and tablet platforms that other Microsoft executives have mentioned repeatedly. The point here is simple: Despite huge growth by Apple’s iOS (iPhone and iPad) and Google’s Android, Windows is still the largest market for apps, by far, thanks to 1.3 billion active users and new sales of several hundred million copies each year.

But PC sales are also growing, contrary to the conventional wisdom. After growing about 2 percent in 2011, the PC market is expected to grow another 5 percent this year, Gartner says. And while tablet sales are experiencing much higher growth, that market is of course much smaller and less mature, too; these factors make faster growth much easier to achieve.

This year, hardware makers are expected to ship about 100 million tablets worldwide, a figure that is well under one-third the ship rate for “old fashioned” PCs. In 2011, 64 million tablets were sold.

Meanwhile, Microsoft is hedging its bets. The company is racing to finalize Windows 8, a new OS that will bridge the tablet and PC worlds, providing a single product, essentially, and a single user experience that works on both types of devices. A near-final release preview of Windows 8 is expected in early June.