A WEEK may be a long time in politics, but two years in publishing is a geological age. At the beginning of 1997 nobody had heard of Joanne Rowling, although a few had spotted her writing in Edinburgh cafes, baby in a pram at her side. Two years later, however, this coffee-house scribbler is being mentioned in the same breath as CS Lewis, Roald Dahl and Robert Louis Stevenson. Her spirited hero Harry Potter, ordinary boy turned wizard, who takes on the forces of evil, is almost as famous as Aslan the lion, Willy Wonka and Jim Hawkins.

Rowling cringes at being ranked alongside such giants of children's fiction, yet the evidence from bestseller lists and literary prizes across the world suggests such comparisons are not as absurd as they may sound.

A lively young woman of 33, Joanne Rowling neither looks nor behaves like an international superstar. Her face is pointed like a cat's, her eyes are bright, and she has shoulder-length auburn hair that has a supernatural shine. It doesn't take much imagination to picture her as a professor at her famous Hogwart's School for Witchcraft and Wizardry. Today she is ethereally pale, having been up all night rewriting a chapter of Harry Potter and the Prisoner of Azkaban, the third in the projected seven-book Harry Potter series.

After the phenomenal success of the first two Harry Potter books, which have led to a film deal with Warner brothers, it's said that JK Rowling will be a millionaire by 40. Yet despite her rags to riches reversal, she has just come into Edinburgh by bus. Clearly the material side of success has yet to permeate.

Friendly and confiding, she bubbles over with conversation and wit. Her publishers may sometimes wish she were less forthcoming, but her openness is part of her restless charm. Not that she doesn't wish that she could at times have fended off media inquiries.

When she first came to fame, Joanne Rowling's story was neatly divided between admiration for the skill of her children's novel, Harry Potter and the Philosopher's Stone, and pity for a plucky single mum, struggling on benefit with a baby. "For a while I thought I was going to vomit if I saw another picture of me captioned with single mother, penniless and divorcee ... Seeing it all down there in black and white you think, Jesus Christ, I'm so sad, amn't I? I don't feel that sad."

Sad, though, is the last word to apply to a woman whose success is staggering. The week we met, she had just learned she was in the New York Times bestseller hardback list, both adult and children's. Unlike some writers who claim that winning literary prizes is irrelevant, Rowling was delighted when Harry Potter snaffled the Smarties Prize, twice in succession. This week, she will discover whether she is also to take the coveted Whitbread Children's Book of the Year. Before a recent change in the rules, the winner of this section would have been eligible to win the overall Whitbread Prize. Even then, she doesn't think she would have taken it. "Children's books generally are very sidelined. I don't think I'd have had a chance in hell of winning it."

Yet you can imagine that it might have happened. Since his first appearance in 1997, Harry Potter has moved beyond the realm of children's literature into the adult world. There's something about this lovable, pert and thoughtful youngster that catches the attention.

In this tale there's a hook for every imagination. A straightforward battle between good and evil, the Harry Potter books engage at a deep level, both morally and emotionally. And a large part of their success is their humour, the sharp one-liners and rumbustious ridicule that set the story alight.

Harry's famous first trip to Hogwarts by steam train from King's Cross is a journey that has a special resonance for Rowling. Her parents met on a train from London to Edinburgh, and later returned to Scotland for a secret marriage at Gretna Green. Rowling's grandmother was illegitimate, born of Scottish parents, but abandoned in a London nursing home, whose owners adopted her. She was privately schooled and, until she was 14, lawyers used to visit her every year. Whoever her parents were, one of them had money.

When Rowling's marriage broke up, she made for Edinburgh, where her sister Di lives. Now she feels "an increasing allegiance to Scotland". She recalls a timely Scottish Arts Council grant of £8,000: "I'm never going to forget that as long as I live," and her daughter Jessica is now at school in Edinburgh. "I feel we've really put down roots here. This is now my home. Full stop."

Rowling's background, however, is firmly English. She spent her first nine years in Bristol, where she played with a gang of friends, among whom were two whose surname was Potter. Then her father got a job at Rolls-Royce, and they moved to a house by the Forest of Dean, near Chepstow, close to Wales and its legends and wilderness.

"Living in this really rural area, where there was very little to do -- beautiful wild scenery and so on -- I think it really stimulated my imagination, definitely, just because we couldn't go to the cinema, we couldn't do what a lot of urban kids do, so we were out making up ridiculous things in the fields."

Though the setting was an influence on her work, only one character in the books is directly drawn from the Forest of Dean: Hagrid, the enormous Keeper of the Keys, whose dropped word-endings are a Chepstow speciality. In shape he's modelled on the Welsh chapter of Hells Angels who'd swoop down on the town and hog the bar, "huge mountains of leather and hair".

Asked constantly about the source of her books, Rowling can only say "I get it all from remembering what it was like to be a kida So everything Harry goes through, and all these feelings of being lost sometimes and confused, these are all things I remember really vividly".

From the earliest age Rowling was writing fiction. She told her sister stories - "endlessly, poor thing" - and made up serial tales for her school and university friends. There are two adult novels in a drawer, "which are due to be destroyed any moment ... they were a bit crap. Very crap."

Once Harry Potter came into her head, however, she grew very excited, not to say possessed: "It's definitely a compulsion. I might go really round the twist, more so than maybe I am already, if I couldn't write."

From the start, the world of Harry and Hogwarts took her over. "My terror when I first met the publisher after they'd taken the book was that they wouldn't ask for sequels. Because I had seven mapped, and I had boxloads of stuff on Harry." Already, she's writing Book Four, and the last chapter of the last book has been written. "I've seriously started thinking I should lock it up and put it in the attic, because no-one must know what happens at the end. It's crucial."

When she talks of Harry Potter, his imagined life is clearly more interesting to her than her own. She talks as though he's within earshot: respectfully and with affection: "Harry is changing as he's getting older. He and his friends are 14 now and their hormones are kicking in, so it's really fun to write about. Everyone's in love with the wrong person, it's brilliant."

The staggering success of her books has left Rowling amazed, and grateful. Although the early publicity provoked her first-ever bout of writer's block, when she was well into Book Two, she doesn't believe Harry has been in any way altered by her fame: "I truly don't think that Harry has been in the slightest affected by anything that's happened to me because the roots go too deep. So when I sit down to write about him, none of that intrudes."

It's obvious that Harry is as dear to her as a son, and she talks about nothing, save her daughter, with such love. There's no exaggeration, you can tell, when she wistfully says: "He feels so real to me, I think it's going to break my heart to stop writing about him."