IT WAS the tabloid story that no editor could resist. When a photo of Peaches Geldof purportedly "taking drugs" appeared on the editorial desk, it must have been too tempting to turn down.
The wild-child daughter of saintly Sir Bob and rock-rebel drug-overdose victim Paula Yates pictured snorting coke? It was red-top, sales-shifting dynamite.
The shot apparently showed a friend holding a makeshift drug-snorting device to Peaches' nose - but it looked more like an unfortunate camera angle than anything else. And if she really was taking cocaine, it was a spectacularly awkward way to go about it.
But she wasn't taking drugs. Her dad came out the next day and said he knew she wasn't taking drugs. The friend pictured with her said he was appalled at the suggestion and insisted that neither he nor Peaches ever took drugs. He insisted that he had just been passing her a roll-up cigarette.
On this occasion, she was in the clear.
But the question Bob Geldof may well be asking himself now is: Is Peaches going down the same road as her mother? Does the second of Bob and Paula's three daughters see her mother as a role model? And if so, will it be possible to stop a precocious teenager emulating her wayward - but undoubtedly cool - mother, who lived fast and died young?
While the "drugs" pictures may have been misinterpreted, Peaches' increasingly rebellious behaviour in the past year or two must be of great concern to her father.
She drinks and smokes. She plays in a DJ group called Trash Pussies. She hangs out with the hip gang in Ibiza and London. She is always partying. She is pretty and pouting and has famous parents and likes to "perve over" rock boys such as Pete Doherty and Russell Brand. She earns lots of money from Sky documentaries and writing magazine columns. She's cooler than Kate Moss and she's only half her age.
In fact, at just 17, Peaches Geldof is already as famous as her mother. She has grown up too fast. Whether she follows the same path as her mother remains to be seen. But she appears as if she is perchedprecariously on that slippery slope.
Because the pattern of wild-child celebrities giving birth to wild-child children is nothing new. It has been going on since the days of Ryan O'Neal and daughter Tatum; Donald Sutherland and son Kiefer. More recently in Britain, Amanda de Cadenet, daughter of racing-car driver Alain de Cadenet, was the original wild child.
In the UK, there is a whole generation of young stars who are like crazier, full-powered, 21st-century versions of their mothers and fathers.
One of Peaches' adversaries on the London rock scene is "edgy" young popstar Lily Allen, the only girl capable of stealing her Teen Queen crown.
Lily is the daughter of rebel actor Keith Allen and has already spoken publicly about her wild life, saying she first took ecstasy at 13.
According to the gossips, Lily and Peaches hate each other, after Lily called Bob Geldof a hypocrite and Peaches responded by describing the singer as "Lily 'Cokehead' Allen".
It was a reference to an interview Lily gave in which she said she would celebrate her single, Smile, reaching the top of the charts by "doing gak" (a line of either meth or coke), a comment she later claimed was a joke.
Ozzy Osbourne once said that he spent the best part of his life addicted to drugs and alcohol. So maybe it should come as no surprise that both his children, Kelly and Jack, ended up in rehab before they were even out of their teens.
Jack was the first to go with a spell in rehab for addiction to painkillers, alcohol and marijuana; Kelly followed shortly afterwards, admitting to a painkiller addiction.
Undoubtedly, many children - celebrity or otherwise - grow up to copy the behaviour they see in the home.
But then again, some celebrity parents can be unlucky, even after being the perfect role model for their children.
Pierce Brosnan, who took on his wife Cassandra's children after she died, provided a stable life for son, Chris, to no great advantage.
The Hollywood actor, who is from Navan, Co Meath, threatened to disown Chris if he didn't kick his spiralling heroin addiction. Chris managed to do so - and his stepdad's celebrity no doubt helped him to land on his feet as a contestant on TV's Love Island. He was voted off the show last Monday.