The Hobbit is definitely going out of theaters, at least in the USA. There will still be second-run theaters showing it after it goes out of first run, but there aren't that many second-run houses anymore.

My impression is that it won't run as long as some of the other top releases of 2012. Marvel's The Avengers is the top, at a billion and a half dollars worldwide. It stayed in release 154 days. The Dark Knight Rises, number 2, was in release 147 days. Number 3, The Hunger Games was in theaters for 168 days. Then there's Skyfall at number 4, only 80 days. The Hobbit is number 5, at 48 days and counting. Next is The Twilight Saga: Breaking Dawn Part 2, which ran for 76 days.

My impression is that The Hobbit will be roughly as successful as Skyfall (which didn't have the advantage of ticket surcharges for 3D). In dollars adjusted for inflation, all three of the LOTR parts did better at the box office, especially in the USA.

My suspicion is that Warner Bros. is pushing toward the DVD/Blu-ray/VOD releases because they know that will make them more money than the theatrical take. As jtarkey says, the studios are fiddling with the "windows" between theatrical release and release on other "platforms."

The Fellowship of the Ring, by the way, was in release for 243 days. Released mid-December 2001, went out of theaters in mid-August 2002, two weeks after the release of the theatrical-version DVD. That shows you how much things have changed in a little over a decade.

If you want information of this sort, it's available at BoxOfficeMojo. Just type a film title into the search box, and you'll get all sort of information about lengths of runs, how many theaters, box-office figures, and more.