Mayors in three of New Zealand's poorest districts - the Far North, Rotorua and Gisborne - want to take over central government agencies in their areas to eradicate "entrenched poverty".

The three mayors have written to Prime Minister Bill English proposing "demarcation zones" in their districts to try new ideas in welfare, health, education, employment and policing.

Gisborne Mayor Meng Foon said Mr English was "very warm" towards their ideas, which tie in with local trials already under way based on English's "social investment" approach.

Far North Mayor John Carter said "subcultures of poverty" persisted in all three areas despite years of central government programmes.

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"Our failure to deal with entrenched poverty means we are turning our young people into unskilled dependants and, in some cases, drug addicts, gang members and criminals," he said.

He quoted one family of a grandfather, grandmother, five adult children, their partners and children who had amassed 669 criminal charges between them.

"Between the five children and their partners they have eight children, none of whom go to school," he said.

"Imagine if you will what happens in another 15 or less years when these eight children start having children and there are now a greater number as the generations increase in number. Where do they go?

"Straight into our back windows!"

The three mayors each have different ideas on how to tackle the problem, but all want to take more responsibility locally away from central agencies.

Mr Carter said the Far North wanted to change the welfare system "from an as of right system to one of a reward system".

He called for bringing back 1980s-style work schemes to employ the unemployed on community projects such as "footpaths, toilets and other amenities, stream clearing, pruning in the forests, conservation projects, elderly and community gardens".

Mr Foon said Gisborne was lobbying Finance Minister Steven Joyce for it to become a special economic zone with low tax rates to boost jobs.

Rotorua Mayor Steve Chadwick said she had asked Social Development Minister Anne Tolley to devolve social services funding to a local leadership group that she has already set up with the local heads of government agencies and the Lakes District Health Board.

Social investment "place-based approaches" have already been started in Northland led by the Education Ministry, in Gisborne led by Mrs Tolley's Social Development Ministry and in South Auckland led by the State Services Commission.

The idea of "demarcation zones" in the Far North, Rotorua and Gisborne came out of workshops organised by Wellington-based think tank the McGuinness Institute, which was supported by the Treasury to run groups in five districts.

Its proposal said similar special economic zones in parts of China, such as Shenzhen, hugely increased local incomes.

The report proposed to "decentralise control by empowering local officials and/or establishing a decision-making governance board of people who reside in the area".

"Small isolated areas are easier and cheaper to experiment in, with clearer results as to which reforms are and are not working."