You may have heard about Avatar. James Cameron’s 3D juggernaut has reportedly topped $2b globally as of this weekend, and seems poised to dominate the box office for weeks to come. 3D showings are sold out days in advance in major cities, and there’s every reason to believe that the film has at least another month’s worth of box-office fuel in the tank.

But there are only so many 3D screens to go around. So what happens when Disney releases the 3D Alice in Wonderland on March 5? Which movie gets the limited number of 3D screens?

The New York Times reports on the possible bottleneck faced by Fox and Disney. With at least 70% of Avatar’s revenue coming from 3D exhibition, Fox doesn’t want to lose a screen. But the IMAX chain has already promised most of its 179 domestic and 82 foreign 3D screens to Disney for Alice in Wonderland. If Alice doesn’t perform, Fox could get some of those back in a hurry. But if the interest in 3D ignited by Avatar turns into big money for Alice, will March 5 be the end of the line for Cameron’s film?

This situation is going to crop up again soon afterward, as Dreamworks releases How to Train Your Dragon in 3D on March 26. Warner Bros. and the 3D conversion of Clash of the Titans will be hot on that movie’s heels on April 2. What irony that studios, chasing extra revenue from 3D, could be hamstrung by competitors racing for the same brass ring?

We’ve seen these 3D bottlenecks before. Early in 2009 Coraline was bumped from 3D screens by The Jonas Brothers. But when that musical movie failed to do any big business, 3D screens were taken back by Coraline a couple weeks later. As studios rush 3D productions out the door there will be less and less opportunity for a film to reclaim screens. Within the next year there’s always going to be a new 3D release waiting in the wings every few weeks.

Within months we’re likely to see theater chains installing more 3D screens to accommodate the increased flow of 3D product (that word ‘product’ seeming so appropriate in this case) but how long will that take? RealD reportedly has 5,000 contracted screen installations, but is waiting for money to fulfill those contracts. Studios have been reluctant to help theater chains invest in 3D upgrades so far. Could that stance be reconsidered? The National Association of Theater Owners says that by the end of 2010 there will be 5,100 3D screens in the US, but that is still a small number if movies are going to be jostling up against one another competing for screens.