THE world of celebrity is often a rocky path for the offspring of the rich and famous, who find the success of their parents a difficult act to follow.

They may have the advantage of material wealth and a luxury lifestyle, but they also have to share their parents with fans and the general public and often have to endure long periods when one or both parents is absent.

But there are kids who make good such as the children of Jack Straw, Jimmy Tarbuck and Dennis Waterman.

And they have not always chosen the same career path as their parents. Anita Roddick's daughter, Sam, for instance, is opening a sex shop in London with her mother's approval.

In fact, her mother will be among the family members who will be helping out on the shop floor initially.

Other members of the younger generation have chosen the same career as their famous parents.

Hannah Waterman, daughter of Minder star Dennis Waterman, has found success in acting, as Ian Beale's downtrodden wife Laura in the hit soap EastEnders.

The 25-year-old actress, who is extremely close to her father, says she had a great time growing up despite the fact that her father split up from her mother, his second wife, actress Patricia Maynard, when she was a child.

''When I was young I thought everyone had a famous dad because all our friends had famous dads too and our house was always full of people I'd seen on TV. I had a great time growing up.''

Both parents were against Hannah becoming an actress, but she was determined and is now reaping the rewards.

DOWN-to-earth Liza Tarbuck, currently starring as the eponymous Linda Green in the BBC1 comedy drama series, went through a rebellious period growing up with her famous comedian dad, but now reflects that the restrictions set by her parents probably did her good.

''Dad was a strict disciplinarian. If you did bad things you were grounded and he was quite tight with pocket money. I had to clean the boot of his car or things like that.

''But that forced me to go out and get a job so I didn't have to ask for anything. That has been one of the driving forces in my life. I would not ask my parents for something because it would be too easy.''

She admits in some ways the showbusiness world had a negative affect on her childhood.

''Growing up with a famous parent does make you angry sometimes. Your home life is known to other people so you are at a disadvantage as they have already assumed what you are before they meet you.

''As a kid I got invited to friends' places so their parents could say, 'You know who that is?' or because they hoped dad would come and pick me up.

''Later on that made me quite angry and marginally paranoid in my late teens.''

Other children simply show similar talent to their famous mothers and fathers.

William Straw, aged 21, son of Foreign Secretary Jack Straw, has recently been elected President of the Oxford University Student Union, a post he will take up next June.

He won the post as an independent there was no Labour candidate in the race - and has a reputation as a student activist, much as his father had when he led the National Union of Students in the 70s.

Children of famous people often do better if they achieve success in a different field to their parents, says psychologist Andy Evans, author of Fame, The Psychology of Stardom.

''It's better to work in a different field because you have more space of your own, as has happened with Stella McCartney, who has become a successful fashion designer,'' he says.

''In that way people don't make comparisons, saying they aren't as good as their parents, or that they only got there because of their parents.''

Jade Jagger, daughter of Mick and Bianca Jagger, became a wild child and was expelled from public school before going into modelling and art and is now a successful jewellery designer.

CRUCIALLY, her parents divorced when she was seven and Jade grew up torn between rock excess and a yearning for the domestic bliss she'd missed out on.

''Any psychologist would say I wasn't fully satisfied with my family and I wanted to build up my own,'' she explained. ''I'd been left to my own devices far too much.''

Other children of famous parents have gone off the rails during their adolescence - Victoria Sellers (daughter of Peter Sellers and Britt Ekland), Carrie Fisher (daughter of Debbie Reynolds and Eddie Fisher) and Liza Minnelli (daughter of Judy Garland and Vincent Minnelli) all spiralled into phases of drugs and drink, unable to cope with their lifestyles.

''Lots of celebrities are very self-occupied. There are cases of relative neglect from some showbiz parents,'' Evans notes.

Whether the children of celebrities achieve success in their own right and come out unaffected by the world of showbiz largely depends on the strength and guidance of the parent who remains at home, he adds.

''Many children have to endure long periods when one parent is absent, pursuing their career,'' said Evans.