Harry Potter is growing up, and so is his movie franchise.

Under the tutelage of a new director -- Alfonso Cuarón, known for both children's fare (the 1995 remake of "A Little Princess") and an edgy, insightfully soulful, sex-charged teen road-trip flick ("Y Tu Mama, Tambien") -- the boy wizard has graduated from the world of kiddie movie spectacles with tie-in toys.

"Harry Potter and the Prisoner of Azkaban" is a film in which depth of character, cunning humor and hair-raising chills come shining through the visual blitzkrieg of special effects -- which are also magnificently improved over the series first two installments. Case in point: a half-horse, half-eagle creature called a Hippogriff that gives "Lord of the Rings'" Gollum a run for his money as the most life-like CGI creation in cinema history.

Beyond just its detailed feathers (which fluff when it shakes) or its golden eyes (which bore holes in the screen with obstinate personality), this winged equine's every movement, from its canter to its peck, is a studied yet natural, amazingly fluid amalgam of the two beasts that were combined to create it.

More nebulous but no less realistic are the terrifying Dementors -- towering, faceless, floating Grim-Reaper-like ghosts whose tattered, wind-blown robes give the appearance of hellish jellyfish. They play an integral part in the plot, hunting for a dark wizard named Sirius Black (Gary Oldman), the only inmate ever to escape the legendary lock-up that gives the film its title.

Black's breakout threatens not only Hogwarts School of Witchcraft and Wizardry, but Harry Potter in particular. He soon learns this villain was once a friend of his murdered parents and is thought to be the Judas responsible for leading them to their deaths at the hands of the as-yet-unseen, uber-warlock Lord Voldemort.

Having finally pent up enough fury and pubescent petulance to stand up to his horrible muggle aunt and uncle, the film begins with Harry (Daniel Radcliffe) illegally using magic to wreak a little havoc on their restrictive household before packing off trans-dimensionally for another year at Hogwarts.

Older, bolder and more pro-active, in this movie Harry becomes a real hero under whose chest beats the strong, if seething and bewildered, heart of a lion. When he discovers Black's history Harry declares, "I hope he finds me! Because when he does, I'm gonna be ready. When he does, I'm gonna kill him!"

Thanks to the growing talent of Radcliffe, who has become more natural and engaging with each "Potter" picture, this moment is riveting to a character-defining degree. There's no doubt he means it, even if we and he both know deep down the boy is ill-prepared for such a showdown -- and there's no doubt we're seeing a Harry Potter who is leaving preadolescence behind.

Harry's best friends, cheeky over-achiever Hermione and misfit redhead Ron, and the young actors who play them, Emma Watson and Rubert Grint, have grown as well, which helps Cuarón and screenwriter Steve Cloves to dispense with exposition and get down to real character development.

This is especially true of scenes in which Harry bonds with the school's latest Defense Against the Dark Arts teacher, Professor Lupin (the sublimely elusive David Thewlis), who was a dear friend of the young wizard's parents and who teaches Harry protective incantations to use against the indiscriminately dangerous, fear-feeding Dementors. But Lupin may not be what he seems.

While holding fast to the spirit of the "Harry Potter" books and films -- complete with the deliciously astute scenery-chewing of Alan Rickman as ominous Professor Snape and the usual grand performances from Maggie Smith (persnickety Professor McGonagall) and Robbie Coltrane (mountainous, soft-hearted handyman Hagrid) -- in Cuarón's hands an artful evolution takes place that transcends the franchise's popular appeal. This film is intelligent and incisive, especially in its execution of author J.K. Rowling's trademark plot twists. It has a shadowy, otherworldly style that doesn't feel market-tested and pre-packaged for the lowest common denominator.

And yet, it's the most accessibly engaging and amusing of the three "Potter" films so far, beginning with its very first chapter, in which Harry boards a magic, invisible-to-muggles triple-decker bus after leaving home, which takes him on a wild amusement-park-like ride careening through the streets of London.

Nearly every scene in Hogwarts is packed with background humor (often thanks to the school's living paintings), and the movie is blessed with an ingenious, scene-stealing turn from Emma Thompson ("Sense and Sensibility") as Divination Professor Trelawney, a tactless, off-kilter, hocus-pocus hippie who teaches crystal-ball and tea-leaf reading. (Stepping in for the late Richard Harris, Michael Gambon is also delightful as a familiar, yet delightfully different, headmaster Dumbledore.)

The handful of problems "Azkaban" has are actually inherent to the story -- a few plot developments inspire "why don't they just...?" questions, the beginning of the third act gets briefly lost in a lull of its own convolutions, and school bully Draco Malfoy (Tom Felton) now seems like too much of a scaredy-cat to rouse any respect from his cronies or fear from anyone else.

But Cuarón's command of the story is so strong that he barely blinks as he steers a course through these minor obstacles, which are no worse than the ones that sometimes tripped up the series' first two installments, directed with charm but considerably less savoir-faire by "Home Alone's" Chris Columbus.

This is far and away the best "Harry Potter" movie yet. But one word of warning to parents of small children: It's also the scariest.