Now, two children later (Lily-Rose, five, and Jack, one), he's full-on with fatherhood, saying that the birth of his little girl was 'not just the greatest thing that's ever happened to me - it's the only thing that's ever happened to me. I helped give our daughter life, and I feel she gave me life'.

He's warm, but not soft. He has a rip in his jeans that reeks rock'n'roll hero, and we're sitting in a smart hotel room in Los Angeles that must be similar to the room at The Mark hotel in Manhattan that he famously trashed. 'I was having a bad day. Those days happen. Some guys hit things, bust something up, or go to the gym and take it out on the hitting bag. Had that hotel installed a bag, we'd never have had a problem,' he says, with a very sweet smile revealing four glittery gold teeth that he had fitted for his role in Pirates of the Caribbean: the Curse of the Black Pearl.

There are many myths about him that turn out to be true, such as the one about him chasing some paparazzi down a street with a large block of wood. 'I asked the cops if I could have the block of wood back at the end of my little stint in the custody suites. They wouldn't let me have it. It was well worth it, going to jail that night. I didn't mind.' He settles into telling the tale of that night. He tells it like a bedtime story.

'It was an invasion. To make a long story short, my girl and I were in London. I was doing Sleepy Hollow. We had some friends who'd come in from Texas. My girl was six months pregnant and we were celebrating the fact that we were going to have a baby. Somebody recommended this restaurant [Mirabelle], so we went there, and there was wine and we drank the wine. We were about to leave, and someone came up and said, 'Listen, there's a gaggle of paparazzi outside, so if you go through the kitchen, we can take you out of a side door.' And I said, 'Let's do that.' But they were waiting for us, so I said to Vanessa, 'I'm going to keep them busy. You guys go around to the front and get in the car and I'll stop them getting a photograph of the belly,' because that's what they wanted, that's where the money is.

'I told them, 'Listen, I know the photograph you want. You're not going to get it. Not tonight. Just let it go tonight. I don't want to be a novelty tonight.' They were really rude and said, 'We're going to get the picture. You can't escape,' and it just happened that there was this block of wood on the ground. I guess it was a doorjamb, so I grabbed it, and the guy who was trying to pull the door open, I smacked his hand with the wood.

He recoiled, and I said, 'Now I want you to take a picture. I'm going to cave in your skull with this hunk of wood,' and miraculously, no one took my photograph. It was becoming more surreal. I made them walk backwards down the street because I wanted to humiliate them. So they walked backwards, they looked really stupid, and I guess one of them had made a call to the cops. As soon as the cops arrived, they started taking photographs again, but it was worth it. Surreal, poetic, fun.'

All this because he didn't want to be a novelty, a product. He's said that before, many times. When he first got into acting, it was something that he did while he was trying to make his rock'n'roll band, the Kids, work out, but he never got a deal. He got a part as a clean-cut cop, the good guy, sexy and cute, always very clean, in the TV series 21 Jump Street. He hated being this cutesy.

He wrote later that he felt 'plastered, postered, postured, patented and plastic, stapled to a box of cereal, novelty boy, franchise boy, no escape'. He wrote this in the foreword to Burton on Burton, the autobiography of Tim Burton, who directed Depp in the lead roles of Edward Scissorhands and Sleepy Hollow, and was his way out.'Well,' says Depp now, rolling up another cigarette in brown liquorice paper. 'I haven't had so many bleak periods lately. Becoming a dad, you don't. It was something that was frustrating when it mattered.' And now it doesn't matter so much, being a product? 'Not so much. Kids give you that kind of perspective, that kind of strength. It mattered before, the idea that whatever you do, you were just this thing.'

The contradiction of doting daddy and wild man sit very comfortably within him. He's part Cherokee Indian, 40 years old, but looks about 30. In the movie, he has decorated dreadlocks and a very fancy goatee. In real life, he has longish hair, below chin-length, one of those knitted fez hats, dark-rimmed glasses, trimmed-up facial hair, a few raggedy layers of shirt, and skull-and-crossbones rings. His childhood was more gypsy than pirate; the youngest of four, born to working-class parents in Kentucky, eventually shimmying down to Florida, not making friends easily because he preferred to be weird. He saw a fire-eater at a circus and, at 12, he almost set himself ablaze trying to emulate the act. He has often said he's really only a musician and everything else about his career was an accident.

'When I was a little kid, that was always my dream. I remember when I was 12 years old, puberty kicking in. You start to get interested in girls and things are going on in school and there's weirdness in your home life and you're embarrassed to be seen with your parents. That's when I got a guitar and everything else disappeared. It saved me. I locked myself in my room and taught myself how to play. Of course, that 12-year-old kid is enthusiastic about rock'n'roll, but it was really just about the playing. That was the great escape for me.'

He was 15 when his parents split up, and he says: 'I was pretty much ready to leave myself, and did so not long after that. They'd had a fairly prickly relationship for a number of years, so on the one hand it was a relief, and on the other hand it was a radical change for my mum and she got very ill, so there was never any time for that kid to feel bad about his parents splitting up because the kid in me had to go straight for the mum, to look after her, to make sure she was going to be okay. But that happens with me, wanting to take care of people, make sure that everybody's okay.'

Johnny Depp got married when he was 20, to a make-up artist called Lori Allison. 'Yes, it just kind of happened. It seemed the right thing to do at the time, but at 20 years old, you're kids.'