In-demand state secondary schools want the Government to let them accept children of former students who live outside the zone.

Each year, some of Auckland's top schools including Auckland Grammar School, Epsom Girls Grammar School and Mount Albert Grammar School have to turn away students with family connections.

Auckland Grammar headmaster John Morris said that in doing so, schools were losing their history and character.

"The current legislation, by not prioritising the sons of old boys to attend the school, is breaking those historical inter-generational links, which in my mind is very sad," he said.

Old boys showed their support for their school through donations and involvement with the board of trustees, parent-teacher associations and sports teams - but were unlikely to offer this if their boys were turned away, he said.

Denying access to families was "a serious oversight".

He and other principals hope the Government, which has indicated it is more open to choice and flexibility, will at least be open to discussion.

Under the zoning system, introduced in 1999, popular schools must take students who live within their zones.

Applications from outside the zone go into a ballot.

The ballot is drawn under the supervision of a police officer, solicitor or justice of the peace, and if the son of an old boy is selected from the ballot it is purely by chance.

Mr Morris said these regulations had pushed up the value of "Grammar zone" homes, and had caused a drop in the percentage of Maori and Pacific Island students at the school.

He said that figure was now 3.5 per cent; it was about 10 per cent when he joined the school in 1993.

Mr Morris would also like principals to have greater flexibility in selecting out-of-zone students to better represent Auckland's ethnic composition.

Mount Albert Grammar School headmaster Dale Burden said it was heartbreaking to have to tell a former pupil that their son or daughter had not made the cut.

He hoped Education Minister Anne Tolley would be open to helping schools with a strong history to keep out-of-zone families at the school.

But he said the rights of local families to attend local schools should not be changed: "If you can walk here you should be able to go here."

Labour's education spokesman - and former minister - Chris Carter said the zoning laws the Labour-led Government brought in were fair and transparent. Before the changes some schools were half-empty and wasting resources while others were growing at a phenomenal rate and costing the taxpayer.

Weakening the zoning requirements would cause the same situation.

"I don't think that's a very sensible approach to a comprehensive, quality education system."

Ms Tolley could not be reached for comment.