LOS ANGELES — Will it soon be time for 20th Century Fox’s “Avatar” to surrender the 3-D stage? Walt Disney Studios certainly thinks so.

“Alice in Wonderland,” a 3-D adaptation from Tim Burton and Disney, is set to replace “Avatar” in all commercial Imax theaters and in many multiplexes that operate 3-D screens on March 5.

The problem is that “Avatar” is still playing like gangbusters — especially in 3-D theaters, which charge premium prices for tickets and have been instrumental in making “Avatar” a box office phenomenon — and exhibitors are grumbling at having to let go of a sure winner to pick up an uncertain new prospect.

Fox executives are now quietly talking about fighting to hold some of the big-format screens for “Avatar,” perhaps by giving more favorable financial terms to theater owners who keep it. Disney is set to take over the 3-D real estate just two days before the Academy Awards, a situation that would make it hard for “Avatar” — a front-runner for best picture — to get the traditional Oscar box office bump.

A similar showdown is brewing between, on the one side, DreamWorks Animation and Paramount Pictures, which plan to release the animated “How to Train Your Dragon” in 3-D on March 26, and, on the other side, Warner Brothers. Warner has just decided to convert its sword-and-sandals fantasy “Clash of the Titans” to a 3-D format and release it on April 2. “How to Train Your Dragon” will have to make do with fewer 3-D seats, which sell for a $3 to $5 premium.

The 3-D bottleneck is likely to grow worse. Michael Lewis, the chief executive of RealD, which equips theaters that account for about 90 percent of 3D screens in the United States, said about 60 films were set for 3-D release over the next three years.

“As audiences experience more 3-D movies, scheduling challenges for theater owners and studios will naturally increase while there is a temporary shortfall of 3-D screens,” Chuck Viane, Disney’s president for distribution, said in a statement. Another Disney executive, who spoke on the condition of anonymity because he was not authorized to comment, said the studio did not see “Avatar” as a problem because early interest in “Alice in Wonderland” was quite strong.

“It will beautifully draft off of ‘Avatar,’ ” the executive said.

Fox, Imax and DreamWorks Animation declined to comment. Spokesmen for the Cinemark and AMC theater chains, which operate 3-D screens, did not return telephone calls. A spokesman for the Regal chain had no comment.

Imax long ago promised almost all of its 179 domestic and 82 foreign theaters to Disney for the opening of “Alice in Wonderland,” which stars Johnny Depp. At the time, few suspected that “Avatar” would still be racking up ticket sales that have made it the best-selling film in history, with more than $1.9 billion at the worldwide box office so far. In fact, the flagship Imax theaters in places like the AMC Loews Lincoln Square in Manhattan are still selling out weekend shows with no sign of a slowdown. More than 70 percent of ticket revenue for “Avatar” has come from 3-D.

The owners of Imax’s commercial theaters appear to be bound by their commitment to Disney — although contracts have often meant less in the world of movie exhibition than pragmatic decisions based on the leverage of the players involved. Under pressure from Fox, for instance, Imax might well ask Disney to permit the large-screen theaters to hang onto “Avatar” for midnight screenings during the three-week run promised to “Alice in Wonderland,” according to one executive who was briefed on the situation but spoke on condition of anonymity to avoid further conflict. Another possibility might be to re-release “Avatar” in the large-screen format sometime later this year.

Disney could have a harder time maintaining its anticipated number of 3-D screens that are not Imax. Decisions about what movies play on those screens are generally made on the local or regional level, based on how well tickets are selling. Given the staying power of “Avatar,” theater owners are speculating that it could monopolize 3-D screens into April. The number of tickets sold for “Avatar” is thus far about the same as that for “Titanic” over the same length of time. “Titanic” ran for nine months after its release in 1997.

The collisions among movie studios for 3-D theaters stems from a shortage of screens equipped with the technology. By year’s end the number of 3-D screens in the United States will have expanded to about 5,100, according to the National Association of Theater Owners. But that is still too few to accommodate dozens of big-budget movies released in the format. Mr. Lewis said his company had contracts to install an additional 5,000 screens worldwide. But much of the expansion, he said, has been waiting for a loosening of capital markets.

Eventually, multiplexes that now operate one or two 3-D screens will have five or six. “By the end of the year, I think it’s going to be a nonissue,” Mr. Lewis said of the shortage.