In the spring of 2002, the Tribeca Film Festival rose from the ashes of Ground Zero. Organized with remarkable speed, it was a gangly, ad hoc affair, but it was popular, profitable, and helped a devastated neighborhood get back on its feet. No film festival has ever been born under such conditions, and only a churl would complain that it was less than an epochal moment for New York film culture. Tribeca wasn’t trying to be a world-class film festival. But what it was trying to be, other than a lavish act of boosterism, was difficult to surmise.

Three years later, it’s clear Tribeca has serious ambitions to be a film festival player – and that it is still something of a muddle. It is devoted to being a family-friendly event, with a full sidebar of children’s movies and a colorful street fair on Greenwich Street (April 30). It’s just as devoted to pushing the envelope (Michael Winterbottom’s “9 Songs,” famously featuring non-simulated sex, will screen; so will the self-explanatory documentary “Gay Sex in the 70’s.”)

There is commitment, at every level of the programming, to movies from around the world. There is an equally strong support of American independent film. With four separate competition categories devoted to short films, the festival isn’t afraid of non-commercial formats. Nor is the avant-garde shut out. Three of the most essential films this year are Peter Hutton’s “Skagafjordur,” a study of Icelandic landscapes, James Benning’s minimalist meditation on “13 Lakes,” and William Greaves’s “Symbiopsychotaxiplasm: Take Two and a Half,” all of which arrived much admired by the experimental set.

Tribeca throws its shoulder behind New York filmmakers, with two competition categories, one for features, one for documentary, devoted entirely to their work. It doesn’t neglect “midnight movies,” or ones that have been restored and “rediscovered.” It is a festival that believes in new media! (Sort of, anyway: An online poll encourages you to vote for “best chick flick” – the winner will screen on May 1). Yet it hasn’t forgotten the good old days: there will be free outdoor screenings at a car-less “Drive In” at the World Financial Center. And this year, Tribeca will also become the world’s premiere showcase for Mongolian romantic comedies and Staten Island cinema verite. Okay, so I made those last two up. But why not? The screenings may take place below Canal Street, but the festival’s identity is all over the map. Although the various categories could use some clarifying – I have no idea what differentiates the “Spotlight” films from those in the “Special Screening” section – there’s nothing wrong with such eclecticism per se. Indeed, Tribeca’s range and versatility pose a healthy challenge to the boutique New York Film Festival.

Tribeca is clearly trying to be a little bit of everything for everyone. But aside from a handful of critics, I don’t know anyone who’s actually gone to a screening. Individual films may attract a certain audience, but Tribeca generates little buzz on the cinephile street.

Festival director Peter Scarlet is doing what he can to change that – every year the program has gotten stronger – but he’s stuck between a couple of rocks (the late winter film festivals) and a very hard place (Cannes).Tribeca loses the creme de la creme of American independent movies to Sundance, though a handful of them trickle into the program anyway. (This year’s notable leftovers include Gregg Araki’s “Mysterious Skin,” David LaChapelle’s “Rize,” and Caveh Zahedi’s “I Am a Sex Addict.”)

Tribeca must also compete with more established, equally expansive festivals in Berlin and Rotterdam (where the Russian oddity “4” was much discussed), as well as the Lincoln Center triple threat of “New Directors/New Films,” “Rendezvous With French Cinema,” and “Film Comment Selects.” This year, the big program of premieres at MoMA has made it even tougher for the new festival on the block to land newsworthy titles.

Against all these obstacles – to say nothing of whatever internal dynamics gave us “Raising Helen” as last year’s egregious opening night film – Tribeca always turns up some great local premieres. Last year it was Manoel De Oliveira’s “A Talking Picture.” This year, for the first time in the festival’s history, they’ve nabbed a genuine coup: Wong Kar-Wai’s wondrous “2046,” one of the most anticipated films of the last five years, will unspool at Tribeca.

To some extent the festival lucked out on good timing: Had the final cut of Mr. Wong’s long-delayed project been ready in time, it surely would have premiered at the New York Film Festival. And the international press isn’t exactly flocking to the Tribeca Grand for a look at Mr. Wong’s latest ravishment, which has been in circulation for almost a year now. Still, those four little numbers add considerable clout to the festival. A couple more titles of this magnitude and Tribeca will be a force to reckon with.

Unfortunately, the “2046”screenings are all sold out, though you might take your chances at the standby line. But there are plenty of other things to take a chance on, from the almost certainly ridiculous (“George Michael: A Different Story”) to the possibly sublime (“Towards Mathilde,” a documentary by Claire Denis about choreographer Mathilde Monnier). Highbrow masochists are directed to “The Tulse Luper Suitcase” – six-and-a-half hours of multi-media intellectualism by Peter Greenaway – while lowbrow genre nerds might like “Night Watch,” a nifty-sounding Russian blockbuster.

While tickets for the majority of titles cost $10, tickets for screenings can be as expensive as $75. Please consult www.tribecafilmfestival.org for theater locations and ticket purchase information before deciding which movies to see.