Henry Winkler, fully booked with the new generation

The 17-strong Hank Zipzer series of books about a dyslexic boy, written by Henry Winkler, aka The Fonz, has sold 2.5m copies in the US, and is on its way to Britain.

The dyslexic Henry Winkler, who played the Fonz, only first read a novel in his 30s but now sells millions of his own, written for children.

What is it so draws celebrities - be they actors, pop stars or news anchors - to the art of children's fiction? Is it because they themselves inhabit a sort of fantasy world? That they are keen to extend their fanbases to a new demographic? Or that they are plain desperate to spread the news of their storytelling genius (discovered, usually, upon the birth of their own children)? Just ask the Fonz, or Henry Winkler, the actor best known for playing the quiffed smoothie in the long-running series Happy Days, whose 17-strong Hank Zipzer series of books about a dyslexic boy has so far sold 2.5 million copies in the US, and is soon to be published in Britain.

He is an unlikely literary figure, having read his first novel in his 30s. But Winkler's calling came from his own experience of dyslexia. "I was in the bottom three per cent at school," he said recently. "I was told I would never achieve." Spurred by his success, he is now embarking on a new project, a series called Ghost Buddy, about a 13-year-old boy and his imaginary best friend. Healthy sales in the celebrity children's fiction category seem guaranteed, given that it is the parents who are the fans and the ones buying the books. But with the market becoming increasingly crowded - Barnes & Noble has a whole section of its website dedicated to the genre, in which you will find works by Whoopie Goldberg, Julie Andrews, Jamie Lee Curtis, Julianne Moore and Brooke Shields - saturation point can't be far off. Not that Madonna appears to have noticed. Her English Rose series of books about the lives of five London schoolgirls has, since the first was published in 2003, extended to 12 volumes.

She, arguably, can be credited with opening the floodgates for the subsequent wave of celebrity-penned children's fiction in the UK. For, hot on her tail were Kylie Minogue, Geri Halliwell, Katie Price and Colleen Rooney, some possibly thanks to a little help, but all with their own pink, spangly tales of princesses and ponies. Despite strong sales, grumbles of discontent could be heard from the "real authors" camp, especially when Price's Perfect Ponies was shortlisted for the WH Smith Children's Book of the Year award in 2008.

While in the UK it seems to be largely entertainers who turn their hand to children's fiction (Paul McCartney, David Walliams, Lenny Henry and Ricky Gervais have also done it), in the United States, well-known figures of a much more eclectic troupe have thrown their hats into the ring. Take, for example, the NBC news anchor Katie Couric, who has written two children's books, The Brand New Kid (2000) and The Blue Ribbon Day (2004); the film director Spike Lee, who also has two books under his belt, Please, Puppy, Please (2005) and Please, Baby, Please (2006); and the former president Jimmy Carter, who published The Little Baby Snoogle-Fleejer, about a young disabled boy, in 2005.

Spoilt for choice we may be, but are any of them actually worth reading? Predictably, it's a mixed bag. Getting the thumbs up from the critics is Jamie Lee Curtis's Is There Really a Human Race? (2006), in which the actress ponders, in lickety-split poetic style, the purpose of humanity (it's more engaging than it sounds). And Julie Andrews's The Great American Mousical, which the Hollywood veteran (and children's book veteran - she has been writing them since 1971) wrote with her daughter about the goings-on at a theatre for mice that exists beneath a real theatre.

Less engaging are Madonna's efforts, which were described by one British critic as "bloated, vapid, frivolous, silly? need I go on?" Similarly with Gloria Estefan's Noelle's Treasure Tale, which even stoops so far as to slip a copy of one of Estefan's records into the front cover. Celebrity children's fiction may seem very 21st-century, but in fact there are precedents - quite successful ones. The child star Shirley Temple published a series of short stories in the 1930s, while the Broadway actress Kay Thompson's books about Eloise, a little girl who lives in the Plaza hotel in New York, are still favourites with children.

The pattern appears to be cyclical. In fact, a glance at the current children's fiction charts shows only a smattering of celebrity books. All the pink ponies and princesses have, it seems, been chased off by a darker force: we never thought we'd say it, but thank goodness for vampires.