Parents are to blame when their children turn out to be juvenile delinquents, researchers have found.

Those who are inconsistent, overbearing and arbitary when they try to lay down the law to children produce conflict and are often unsuccessful in their attempts to control them, according to research by a team at Edinburgh University.

Those who are firm but trust their children and allow them a freer rein have fewer conflicts and produce children less likely to get into trouble, they found.

The academics, using findings from The Edinburgh Study, an ongoing project looking at 4,300 children living in the city who started secondary school in 1998, also concluded that delinquency by the age of 12 or 13 was widespread.

They also suggested that children who had been bullied were more likely to go on and commit offences.

Delinquents tend to commit offences in their own school, neighbourhood or social circle, the study concluded.

Professor David Smith, who led the research team, said: "Parents who trust their children but are firm and active in supervising them have a lower degree of conflict than parents who try and lay down the law."

The least successful kind of parenting involved arbitrary and inconsistent attempts to control children with threats that were not carried out.

"Inconsistent parenting leads the child to conclude that behaving well doesn't get results," he added.

More than half the 12 and 13-year-olds questioned for the Edinburgh Study, which was supported by the Economic and Social Research Council, admitted to two or more "delinquent acts" in the previous year.

Definitions of delinquency include shop lifting, fighting, carrying a weapon, stealing from cars, graffiti and assaults. But smoking and drinking are also associated with delinquency and consumption increases rapidly at the age of 12.

They were more likely to have used illegal drugs or to have smoked or drunk alcohol; eight per cent said they had used substances such as cannabis, glue, gas or speed (amphetamine).

Around half had been victims of bullying, harassment by adults or crime such as theft, robbery, assault, threats or attacks with a weapon.

"Those who have been victimised and also those who offend tend to have slightly lower self-esteem than others," said Prof Smith.

The researchers measured three personality traits - impulsivity, or the inability to control immediate impulses, alienation, which was the belief that the world was against the individual, and self-esteem.

Prof Smith said impulsivity and alienation were strongly linked to both offending and victimisation, helping to explain the relation between the two.

His team was surprised to learn that, while delinquency among boys was twice as common, it actually increased more among girls between 12 and 13.

He said: "We expect the boys and girls to draw further apart later, but in the early teenage period girls develop earlier than boys and one consequence seems to be an earlier 'delinquency spurt' along with an earlier 'growth spurt'.

"In particular, there was a rapid increase in smoking among girls so that by age 13 a higher proportion of girls than boys were smokers."

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Updated: 11.03 Monday, July 23