When I arrive at Fox studios in Los Angeles, the mid-morning sunshine is already crazy-bright. "Go straight ahead till you reach the doughnut," says security guard, gesturing toward a 12ft sculpture honouring Homer Simpson. "And then keep going, past the Star Wars mural, till you get to a row of penguins. Opposite the panguis, there's a hedge sculpted in the shape pf a violin. You should find Mr. Pattinson there." This is the mad, make-believe world that Robert Pattinson now inhabits. He's here doing last-minute voice dubbing, even though it's Sunday and the studious are deserted, because he is currently Britains's highest-paid actor (last year's Sunday Times Rich List put the 24-years-old's worth at £ 13 million) and his work is never done. He is a nice boy from leafy Barnes, west London, who became an international teen idol after his brooding performance in the scarily popular vampire saga Twilight (now a tetralogy). He is the Keanu Reeves of the Facebook generation; Leonardo DiCaprio for age of Twitter. He shaves his sdieburns or has a beer and thousands of fans comment about it. He has even acquired a slightly demeaning nickname: RPattz. But while his character Edward Cullen is doomed to stay 17 for ever, Pattinson is growing up and moving on.

No more blockbuster franchises: he is about to shoot Don DeLillo's Cosmopolis, directed by auteur David Cronenberg ("The novel reads like an incredibly long poem," says Pattinson enthusiastically. "The film's going to be totaly an utterly out there"). He has also stepped into the role of leading man in two films this year, first opposite Reese Witherspoon in the circus epic Water for Elephants, then with Uma Thurman in the Gut de Maupassant adaptation Bel Ami. Older women, as he tells me, are nothing new to him: "Every girl I went out with in my teens was older than me. My first girlfriend was 26, I was 17. Women who were older always seemed more exciting." Because they knew more? "I guess so. I used to think I was a bit of a bad-*** when I was younger. I liked that it annoyed people how much younger I was. I liked walking into a room with a woman and people looking at us and thinking: they do not look like together."

If these women are well-dressed, I can see why observers might make that judgement. Today, Pattinson is wearing tatty vintage sunglasses, black sweatshirt, black T-shirt, black jeans and the unshaven, rumpled air of a man who has woken up to find that his car has already been waiting outside for some time. This happens to him a lot, I think. He dumps his cigarettes, laptop and keys on the table and sighs at his own laziness. "My ideal job would be one day a week. When I first started acting, I'd get one job a year that lasted three months, and then I'd do nothing the rest of the time but I'd have enough money to survive. I'd read all the papers every day, get in a lot of DVDs... That was great." He breaks into a wide-cheekboned smile, eyes heavy-lidded, gentle and slightly feline; like James Dean, without the self-hatred.

He's 24 now, but, perhaps ironically, given his vampiric alter-ego's perpetual teenagedhood, seems younger. His face lights up when he sees his favourite lunch has been delivered to the studio: chicken kebab. “I've got simple tates." He's a sweet, goofy boy, quick to laugh and smile, though he doesn't seem particularly happy. But he is, he says, more content than he used to be. He used to write music as a release (his compositions appeared on the Twilight soundtrack) but hasn't felt the need for a while. "I have to be incredibly depressed to write songs and I'm not. What makes me want to write songs is when I wake up crying. I would have no idea why I was crying, but it made me sad for myself... " And he bursts out laughing.

But the pressure of overnight, global success can't be escaped. The swarm that follows him restricts his choices in many ways. "I'd really really love to do a play in London," he says. "But I'd just be afraid it would turn into an 'NSync concert. Or people would come along expecting it to be something like Twilight. From the little amount of theatre I've done, I know that usually you can feel a push from the audience, who have come along wanting the show to succeed. But when I go to premieres, it's more like the crowd is pulling, really wanting something from you. I always feel completely drained afterwards. It would be very strange and exhausting to have that kind of experience every night on stage."

Despite such fears, he denies that the adulation is really for him. He says he's simply a cipher that makes the frenzy permissible. "It's very clear that people have gone there for an excuse to go crazy. You can't stand around in the street and go crazy but get together with your friends at a Twilight thing and you have an environment where you can." This kind of modest thoughtfulness will probably save his sanity. A little vanity comes with the territory, though and Pattinson prepares for shirtless scenes by "going to the gym for four hours a day. I don't eat at all expect for protein shakes. But I don't understand how you could maintain that all your life. After the scene's done, I don't work out again. It's a ridiculous idea that you're not a proper actor unless you have a six-pack."

Pattinson is currently working a six-day week on film projects and doesn't have a social life, or a place of his own. "I came close to buying a house in Los Angeles, but 20 minutes from signing the contract I freaked out. So I don't own a house or really have a home. It can drive you a bit crazy not having any kind of anchor. Hopefully it will settle down some time soon but for the next few years, I'm going to be filming all over the place. I thought I would get a dog. Then wherever the dog was would kind of be my home."

He adopted Bear, a German shepherd-pitbull crossbreed ("100 pet cent mutt"), from a dog shelter in Louisiana: a canine death row. "Bear was two days away from euthanasia. We thought he was traumatised by his near-death experience." Who's we? Was this a solo rescue mission, or was Pattinson accompanied by a certain elfin co-star? He has long been linked with Kristen Stewart, but adopting a dog together would surely mean they were getting serious. "Well..." He looks flustered. Are you going to be a single parent to Bear? "Um, yes, I guess so." The rumours about their impending marriage aren't true, then? "No they're not. I was told I was meant to be getting married somewhere called 'Napa Valley'. It sounded quite cool. Maybe I will get married there."

The ambiguity that surrounds the relationship status of KStew and RPattz (are they? Aren't they? Do we care? The only thing that's certain is that neither will say one way or the other) conveniently generates a huge amount ofpublicity for their vampire movies. I put it to him that the whole thing is a studio fabrication. "No," he says, kindly but firmly. "Oh no. I'd love it if they tried. If studio tried to get involved with my personal life, I could start messing around with them in return... No. There's nothing nefarious going on, I just don't like people taking my picture. It's not nice when your life becomes someone else's news. Even when you're having a good time and someone takes a picture and days, "Look at them having a good time!" I feel like, it's not your good time." So he isn't working to a careful PR strategy? "People think we have people organising everything, that it's all a publicity stunt. It's not. There is no magical entourage - you're just a person on your own. You have to figure it out."

Despite some 'crazy' Hollywood experiences - such as Will Smith coming up to him on Oscars night, just before he was due to present an award, and advising him, "Don't try to be funny. Don't even think about it. Just be cool" - Pattinson says he doesn't have much fun with his fame. Has he learned about what young Hollywood can get away with? Why doesn't he just freeload and fool around? "It just isn't possible to get away with that stuff with camera phones around. I can't do it. If I have four berrs, I'm destroyed teh entire next day. I just don't understand how these stars used to go on benders all the time." He pauses. "Cocaine. Must be.”

He sends every script to his parents to read ("They always come up with good advice because they think differently from the industry. My dad compares every script to Jaws and Superman...") and still misses his childhood pet, a West Highland terrier called Patty Pattinson - "and her middle name was Pat."

It's not going to do anything to limit his appeal to his legions of fans, but he's almost ridiculously soft-hearted. He was drawn to the film Water for Elephants, he says, because of his grey, wrinkly co-star, an elephant called Tai. "I saw her recenly and she remembered me; at least I think she did. She had a new headpiece on and I said "Nice hat, Tai" and her trunk went up to her head. She's amazing." When asked what the greatest extravagance his not-insignificant pay packet has brought him, he says, "It sounds ridiculous but my dog was sick with a puppy disease called parvo and it was such a relief being able to go into the vet and say, 'I want the best, immediately.'"

Water for Elephants is set during the last American Depression, and Pattinson’s performance is impressively controlled, with a subtle sense of period. "I looked at Gary Cooper films, at his stange and stillness. Camera technique wasn't what it is, and you used to have to stay really still. Acting was much more about your voice. Also, my character is a vet, so there's a calmness to him, as there is with anyone who's good around animals." He and Reese Witherspoon crackle on screen; by his standards, the decade between them is nothing. "She isn't really much older than me at all," he says gallantly. Water for Elephants probably isn't his breakthrough performance - the role that will put paid to his teen-idol reputation - and nor was Little Ashes, in wich he played Salvador Dali with huge panache, but, little by little, Pattinson is emerging out of the box marked 'eye candy'. For now, though, it seems inevitable he will remain tabloid fodder. "Gossip magazines make more money them most movies," he says regretfully, until I pull him up: "not your movies." (The Twilight saga has grossed £ 1.12 billion worldwide - the next film Breaking Dawn Part 1, is out on 12 November.) "Yeah, OK," he laughs.

Even so, there's something slightly lost about Robert Pattinson. "I never get what I want," he sighs at one point. His puppy is sick, he doesn't have a home and, reading between the lines, his love life is looking distinctly grey. The mournful edge in his personality is what makes him so desirable, though - and so romantic. Thank goodness this multi-millioneire matinee idol isn't as pleased with himself as he should be: he'd be unbearable. As it is, he's still an outsider, soft and pliable and modest, still waiting to come out of his shell.

Robert's top albums...
1. Moondance, Van Morrison
2. Night Train, Oscar Peterson
3. Abbey Road, The Beatles