With Lily Allen giving her old man Keith a run for his money and Peaches Geldof earning more column inches than Bob, these daddy's girls are living life in the fast lane - and overtaking their elders. So, who's who?

Lily Allen, 21

Famous family: Her famous pa is actor Keith Allen, currently appearing in BBC drama Robin Hood. The comedian and actor split from her film producer mum Alison when she was little and Lily says her childhood was tough as a result.

'My mum would be on the phone begging my dad for money,' she recalls. 'Mum would get paid to do one job, but it had to last a long time: mortgage, tax and three kids' school fees.'

Hitting the headlines: The mouthy singer has had something to say about everyone, from Victoria Beckham to Madonna, to Kylie. But she insists she isn't riding on the coat tails of her famous dad. 'He's not involved in what I do at all,' says Lily. 'In fact, my dad's never even met anyone from my management or my label. If people want to talk about him, they should probably go and interview him. But I have learnt that speaking about my family upsets them, so I'm not going to do it any more.'

Daddy says: 'I'm going to call my autobiography "By Lily Allen's Dad" because she's more famous than me. I'm really proud of her.'

Nicole Richie, 25

Famous family: Nicole was just three years old when she was adopted by soul singer Lionel Richie and his then-wife Brenda Harvey. Although her godfather is Michael Jackson, her real parents are rumoured to be one of Lionel's former band mates and a stage hand.

Hitting the headlines: The Hollywood 'It girl' first hit the big time starring in The Simple Life with friend Paris Hilton, and was then famous for falling out with the heiress, which meant they had to film a series of the hit TV show separately. Nicole, who has written a novel, made the Top 100 Rich List and was reportedly paid £1.3 million for her Jimmy Choo contract. She is regarded as one of today's skinniest celebrities and her tiny frame is a constant topic of debate.

Daddy says: 'I live in fear that Nicole is going to become the next Princess Diana. Just to give an example of how crazy everything has become: I always know when Nicole is on her way home because she is followed by a helicopter and seven cars. It's harassment.'

Liv Tyler, 29

Famous family: The daughter of Aerosmith rocker Steven Tyler and former Playboy model Bebe Buell, Liv grew up thinking that rock star Todd Rundgren was her father. But when Steven was visiting, Liv noticed that his daughter Mia looked enough like her to be her twin. She confronted her mother, and was told the truth; by the time she was 12 she had taken her father's name.

Hitting the headlines: Liv started her modelling career at the age of 14 but it was her role as Arwen in Lord of the Rings that made her a household name. Now a mother, happily married to British rocker Royston Langdon, Liv also featured in her dad's video for Crazy. She has developed a great relationship with her dad: 'I have these slumber parties with my father when we can't sleep,' she says. 'We stay up all night trading beauty tips. He knows all about the good creams and masks.'

Daddy says: 'Liv is the biggest reason for me changing the way I lived. She is a dream daughter. When she was very young I wasn't sure whether I was the father but, by the time she was eight, I saw my features in hers and I cried. I love her more than anything and have a great relationship with her. We can talk about anything.'

Peaches Geldof, 17

Famous family: Pretty Peaches is the middle daughter of Bob Geldof's three girls with his late wife Paula Yates. Paula died of a drug overdose in 2000 and photos of Peaches looking the worse for wear have prompted comparisons with her tragic mum, who got together with Geldof at 17, and posed naked in Penthouse at 18.

Hitting the headlines: Peaches has become known as a party girl despite not yet being old enough to drink in the UK. After a summer spot as a DJ in Ibiza, she hit the decks at trendy Manchester boutique Cricket last month and is often spotted with a lank young musician hanging off her arm. Last year she beat Keira Knightley and Sienna Miller to be selected as society bible Tatler's most eligible girl in Britain. She has apparently also been earning a name for herself in the media, writing for The Sunday Telegraph and ELLEgirl magazine.

Daddy says: 'She is only 17. I'm pissed off about all the stuff that seems to circulate about her. If she went off the track I would go f***ing ballistic, you know. She's a pain in the arse sometimes, like all kids, but she's all right.'

Kelly Osbourne, 21

Famous family: The daughter of Black Sabbath rocker Ozzy Osbourne and talent show judge Sharon Osbourne, Kelly has made a name for herself as a singer and all-round party girl. Along with her brother Jack, Kelly appeared in reality show The Osbournes when the family decided to let MTV's cameras into their home and their lives.

Hitting the headlines: Since The Osbournes, she has become world famous but has managed to play down her image as a spoiled brat. She has since admitted the pressure of the show prompted her trip to rehab to treat an addiction to painkillers in 2004 (Jack also went in to rehab as a teenager).

'It's what you get. I mean, don't be famous if you don't want it,' she said earlier this year of celebrities who moan about paparazzi. 'Don't spill your beans to everyone, and don't be famous if you don't want some attention. You choose to be a celebrity; it's part of the job.'

Daddy says: 'I'm so glad that she's become a star in her own right.'