Children of celebrities – famous and infamous – have it tough. If they're the children of big stars, they often grow up too quickly, surrounded by drugs, drink and the pressures of their parents' fame.

Paul Newman's son, Scott, died at the age of 28 from an accidental drugs overdose. That tragedy apparently haunted Newman to the end, although he tried to turn it to good by setting up the Scott Newman Center. Gregory Peck's son committed suicide. Kirk Douglas's youngest child, Eric, had a long history of problems: run-ins with police, depression, drink and drug addiction and a stalled career as an actor and stand-up comic. He died, aged only 46, in 2004, by all accounts looking grey, bloated and much older than his age.

Marlon Brando's family has been extremely troubled. Christian Brando, in particular, was a sad case. In 1990, he shot his sister Cheyenne's lover, served time in jail and died last year, aged 49. Officially, he died from pneumonia but, by all accounts, drugs had taken their toll. His sister, by the way, had predeceased him.

The recent Formula One controversy overshadowed another tragedy. Max Mosley's son died of a drug overdose earlier this year at the age of 39. Well, knowing that your grandfather was Britain's most infamous fascist leader might be troubling to some people.

Nothing – at least in Hollywood anyway – rivals the dysfunctional O'Neal family. Last week, Griffin O'Neal was banned from attending Farrah Fawcett's funeral by his father, Ryan O'Neal, with whom he's had a particularly tempestuous – and latterly – non-relationship. "He's not a nice man," said Ryan apropos of his son, Griffin, when asked why he had prevented him from attending the funeral of his long-term girlfriend.

Griffin, of course, had a very different account, describing his father as "a dark man". As a teenager, Griffin's father allegedly knocked his teeth out during a fracas. A couple of years ago, on Fawcett's 60th birthday, his father allegedly turned a gun on him. But, needless to say, their versions of all their altercations – no doubt booze or drug-fuelled – differ. Griffin has also suffered from drug problems and his career has stalled, particularly following his involvement in a 1986 boating accident that killed Francis Ford Coppola's son.

But this is just the beginning of problems in the O'Neal clan. Last year, Ryan O'Neal and his son by Fawcett, Redmond, were arrested and charged after authorities said they found methamphetamine at the actor's Malibu home. Redmond was still in jail at the time of his mother's death but, thankfully, was let out to attend her funeral. His father said in an interview that "Red doesn't really know what he's doing here". (on earth, I suppose he meant). But then again – Who does?

But it doesn't end there. Tatum O'Neal, Griffin's sister, has also had a long history of drug-taking and temperamental problems (hence her nickname of Tantrum). She was the youngest child actress ever to win an Oscar (aged only 10) in Paper Moon, starring alongside her father, but quickly got in bad company. She detailed her own heroin addiction and its effects on her relationship with her children. Her mother died young and – needless to say – she has alleged physical and emotional abuse from her father, much of which she attributed to drug use. Her father, Ryan, has denied these allegations, dismissing them as "malicious lies". In recent interviews – surprise, surprise – Ryan O'Neal says he seldom sees his daughter.

And, guess what, it gets better yet. Tatum O'Neal, desperate to escape her tempestuous background, was probably looking for a calming influence in her life. She needed a serene, peaceful and good-natured partner with whom to face life's ups and downs. So she married John McEnroe.

The common denominator in all these cases is that the children grew up much too quickly and got into booze and drugs far too young. In some cases, of course – although not all – they also had irresponsible parents who failed to shield them from the public eye or introduced them to 'bad stuff'.

Outsiders may think that exposure to violent parents, excessive drug-taking or oceans of booze may lead children to turn their backs on this life and strive for a more equable life. But often that's not the case. Sadly, these children can enter adulthood with very low self-esteem. Perhaps unconsciously, they often choose partners who are themselves violent, or who have addictive personalities. And the spiral never ends.

Children ought to be protected from the spotlight as much as possible. They will have their entire adult life to succumb to the temptations of drink, drugs and the greedy nature of fame. But children should be children. They should have private lives. That's why it was a mistake for Michael Jackson's children to be given the spotlight at his memorial service, even if they wanted to give addresses themselves. Particularly in such a family – where thrusting a child prodigy into stardom and treating him like a performer led to such problems in Michael Jackson's life – one would have thought that the family would have handled the late singer's children with more sensitivity and kept them at a distance from the press and public.

Let's learn the lessons and protect children as much as possible from corrupting influences. And, sadly, perhaps Hollywood parents should study the O'Neal family as a case history of what NOT to do.