Apple CEO Tim Cook, taking his place on the same stage where Steve Jobs first introduced the iPad in 2010, unveiled the third version of the tablet today, adding a higher-resolution display powered by a new custom chip and support for HD video and faster 4G LTE wireless networks.

Just called the iPad (no numbers or modifiers), the new tablet will go on sale March 16 in the U.S. and 11 other countries and territories. The models and pricing matches that of the iPad 2: there are three Wi-Fi versions, starting at $499 for a 16-gigabyte model, and three tablets with Wi-Fi and 4G LTE, starting at $629.

Apple says it’s also going to keep selling the iPad 2, but sell it for $100 less as it tries to keep price-conscious buyers from looking to rival tablets.

Cook started and ended today’s presentation by saying that Apple is leading a post-PC revolution and that the iPad is the “poster child” of that revolution.

“In many ways, the iPad is reinventing portable computing,” said Cook, who served as master of ceremonies for the nearly 90-minute event at the Yerba Buena Center in San Francisco. “When we’re talking about the post-PC world, we’re talking about a world where the PC is no longer the center of your digital world, but rather just a device. We’re talking about a world where your new devices, the devices you use the most, need to be more portable, more personal and dramatically easier to use than any PC has ever been.”

That view is unsurprising given that the iPad is now outselling Apple’s Macintosh computers and was the company’s second-best selling product behind the iPhone last quarter, accounting for 20 percent of revenue.

Apple said it sold 172 million devices last year built on its iOS mobile operating system—the iPhone, iPad and iPod — and they accounted for more than three-quarters of Apple’s sales. Cook, echoing comments he made last month at the Goldman Sachs technology conference, expects that trend to continue as more users opt for Apple’s touch-screen tablet over Macs and other PCs, and as more developers put their time, energy and creativity into creating mobile apps.

It’s not the only one to notice the trend toward tablets. Amazon is winning over users with its Kindle Fire (5.5 million), while Google (with Android) and Microsoft (with its upcoming Windows 8 for touch-screen devices) work to lure device makers, app developers and users to their platforms.

Forrester Research yesterday boosted its forecast for tablet sales, saying it expects 112.5 million people, or 34.3 percent of U.S. adults, will own a tablet by 2016 and that consumers, most of whom use tablets today in their living room, will start taking them to work. Growth outside the U.S. will also be robust, according to Forrester analyst Sarah Rotman Epps.

“Tablets are a global phenomenon,” she said. “U.S. consumers constitute only 43% of Apple’s 55 million iPads sold through the end of its last fiscal quarter, with the rest going to consumers and enterprises in the rest of the 90 countries where the iPad is now sold.”

Cook acknowledged that more than 100 rival tablets went on the market last year, saying that’s why this is the third iteration of the iPad in two years (in fact, Jobs announced the iPad 2 almost exactly a year ago.)