What kind of dad are you? Forceful? Useful? Or just plain embarrassing?

It's official: there are four types of father. Modern dads range from a dying breed of older disciplinarians to classic "new men" who will happily share household chores with their partners, according to the government body set up to promote gender equality.

It's official: there are four types of father. Modern dads range from a dying breed of older disciplinarians to classic "new men" who will happily share household chores with their partners, according to the government body set up to promote gender equality.

The four categories of father are identified in a revealing new study of the changing patterns of family life in modern Britain by the Equal Opportunities Commission. First up is the "Enforcer Dad", the traditionalist with a penchant for strict rules and pocket-money rations who believes his purpose is to provide a stern role model.

"Entertainer Dads" see themselves as the clowns of the family, with a duty to keep their children amused while their mothers do the cleaning and ironing.

Then come the "Useful Dads", who, while they seldom take the initiative when it comes to domestic tasks, are at least willing to pitch in.

Finally, there are the growing number of "Fully Involved Dads", progressives who share responsibility for mundane chores on an equal basis with their partners.

The study, which involved in-depth interviews with 60 fathers and their partners, suggests British men have undergone a profound shift over the past 40 years away from the traditional role of the "head of the family". However, it stresses that, in practice, most modern men still see themselves as breadwinners, because the pace of reform has not caught up with the change in their attitudes and behaviour.

Launching the study, which is published today, Julie Mellor, the EOC's chairwoman, said there could never be true sexual equality until men and women earned equal pay, and childcare provision was radically improved."Mums and dads should be able to choose how they want to share the responsibilities of bringing up children and working outside the home," she said. "But until we have equal pay, decent childcare and more opportunities to work flexible hours, many fathers will continue to find it hard to be there for their children and many women will continue to lose out at work."

Her views were backed up by Tom Beardshaw, campaign manager for the charity Fathers Direct. He said the study's findings suggest parents have become increasingly "pragmatic" about who works and who stays at home to look after the children. Whereas former generations would never have contemplated the idea of women as breadwinners, today's couples are prepared to cast such age-old models aside – provided the mothers are the highest paid. "It's fairly clear from this research that the traditional fathers of 20 or 30 years ago are dying out," he said. "The 'Enforcer Dads' that remain tend to be older men, whereas back then they might have been in the majority.

"What we've got is a drift towards a different type of father, with most falling somewhere between the 'Entertainer' and 'Useful' categories. To move things on further, we need government policy to catch up with what's happening at home.

"The research suggests that, in some ways, women are now wearing the trousers. They are making all sorts of decisions in the home, and men, by and large, are just going along with them."

Mr Beardshaw, whose wife Andrea, a vocal coach, works from home so that she can look after their young child, Cole, two, said major reforms were needed to harness the new spirit of equality.

While he praised some of the Government's most recent family initiatives, he said his main concern was the current limit on paternity leave. By increasing the length of time fathers are allowed to be absent from work after the birth of their children from two weeks to nine months, ministers would be proving that they are serious about equality.

Michael Douglas, actor and movie producer

Children: Cameron, 23, Dylan, two. A third on the way.

He says: "I wasn't really there for Cameron. I was trying to forge a career and my parenting suffered."

They say: "The night we met he said, 'I want to father your children'" – his wife, Catherine Zeta Jones.

Liam Gallagher, lead singer of Oasis

Children: Molly, four, Lennon, three, Gene, one, stepson James, eight.

He says: "You don't go out as much and you spend time with your babies. I get more of a kick out of that than getting pissed in the pub."

They say: "Liam is very, very good with Gene. He has this toy that plays 'Imagine'" – partner Nicole Appleton.

Bob Geldof, singer and producer

Children: Fifi Trixibelle, 19, Peaches, 13, Pixie, 11. Adopted Heavenly Hiraani Tiger Lily, four.

He says: "I am here bankrupting myself because I love my children. And all I want to do is be their dad."

They say: "He has made them very happy" – Belinda Brewin, friend of Geldof's ex-wife Paula Yates.

Jude Law, actor

Children: Rafferty, five, Iris, two, Rudy, one month, and stepson Finlay, 11.

He says: "I get up at eight, boil a couple of eggs for me and Raff, get him ready for school, make his lunch ... walk him to school..."

They say: "Sadie and Jude and myself are still very ambitious people but we live every day for our children." – Gary Kemp, Sadie Frost's ex-husband and father of Finlay.