THE BOY WITH THE MOST beautiful name in Hollywood was once told by an agent to change it to Lenny Williams. More recently, producers have advised him to star in movies about demonic teen-agers who strangle their girlfriends, or in tacky, fast-money Westerns like "The Quick and the Dead," which opened Friday. And it has not been uncommon for strangers to offer him cocaine and heroin at industry parties. In his short career -- he just turned 20 -- Leonardo DiCaprio has seen all the twisted ways people respond to a prodigy's gift: change it, own it. Shooting "The Basketball Diaries," due out in April, he was trailed by flocks of pubescent girls, who recognized him from the sitcom "Growing Pains." A mother who spied him blowing bubbles between takes on location in New Jersey ordered her barely ambulatory toddler to go up and hug the famous young man.

It's not that DiCaprio is magnetic or studly: a growth spurt two years ago left him more gangly than statuesque, and his eyes, though piercing, are vacant. Idling on a playground set, he's unremarkable, an empty vessel; his co-star Mark Wahlberg (formerly Marky Mark of underwear fame) has a far more electric physical presence. But when rehearsal begins, it's DiCaprio you watch: his movements are smallest, his stillness is deepest, his lines are tossed farthest away. His acting is effortless and, in the best way, unschooled -- which may be what makes people behave oddly around him. It's as if he were a talisman, imbued with dark magic. How else to explain his unnerving affinity for troubled characters? Plucked at 17 from the insipid "Growing Pains" to play the abused stepson in "This Boy's Life," he stole the movie from Robert De Niro. Then, as the retarded brother in "What's Eating Gilbert Grape," he transformed a grab bag of schoolyard stereotypes into an achingly lyrical portrait of a misfit. The resulting Academy Award nomination made it official: DiCaprio was being groomed for one of Hollywood's classic scripts, the one in which talent equals torment and youth is public domain.

So far, DiCaprio has managed to resist, but how much resistance is it fair to expect from a kid with plenty of cash and hormones? He acts his age. He tells bathroom jokes, goofs on waiters, dares to be seen with the occasional pimple. Here on the set, as the sun disappears and rain machines start spouting, he rejects the ministrations of a wardrobe person who's trying to drape a coat on him; of course, he gets drenched. He's oblivious, and it's just as well. Better not to think about the millions of dollars riding on him in his first starring role. Until DiCaprio came along, "The Basketball Diaries," Jim Carroll's 1978 memoir of a youth spent on poetry, basketball and drugs, had steadfastly defied translation to the screen -- mostly because there wasn't an actor plausible and strong enough to play the young addict. Well, maybe River Phoenix, some said.

In an industry that eats its young, perhaps it pays not to seem too appetizing. Upon introduction, DiCaprio says only, "How you doin', bro?" then sits by himself in the cold, on a bench, not so much preparing, it appears, as preserving himself for the moment in which it will be safe to be alive. But the director persists in waiting for the "magic hour," that brief time just after sunset when the light has a strange and heartbreaking glow -- a light most familiar to moviegoers not from life but from other movies. And DiCaprio waits too.

"I WAS AT A HALLOWEEN PARTY two years ago, at the house of these twin actors," DiCaprio says, "and I remember it was really dark and everyone was drunk and I was passing through these crowds of people so thick it was almost two lanes of traffic, when I glanced at a guy in a mask and suddenly knew it was River Phoenix. I wanted to reach out and say hello because he was this great mystery and we'd never met and I thought he probably wouldn't blow me off because I'd done stuff by then that was maybe worth watching. But then I got caught in a lane of traffic and slid right past him. The next thing I knew, River had died. That same night."

With its running cadence and predictable ending, DiCaprio's tale of missed opportunity is the Hollywood version of a campfire story, one of many that go like this: Young man, talented, beautiful but damaged, makes too much money, parties all night, gorges on drugs, womanizes, wrecks hotel rooms, drives too fast and courts disaster; the body is found at a hotel, crushed in a car, flat on the sidewalk outside a club. Or: The sweetheart teen, an agent's daughter, blossoms on her sitcom while nearly starving herself to death. Or: The doctor's child, not quite pretty enough to be an actress, retools herself as a Hollywood madam, making money off such men as the above, until she's busted.

These stories are not abstractions to DiCaprio. The Viper Room, where Phoenix died, is owned by Johnny Depp, the star of "Gilbert Grape." The brave little thin girl, Tracey Gold, played opposite him on "Growing Pains"; her father was, until recently, his agent. Even closer to home -- a few yards from a house DiCaprio grew up in -- the cautionary shingle of his pediatrician still hangs: Paul Fleiss, M.D. And now, as if to bring the story of Hollywood tragedy full circle, DiCaprio has been asked to star in a film biography of the prototype, James Dean.