Wellington-based MP Mr Hughes announced he would make Auckland a priority if elected and promised to relocate to New Zealand's biggest city with his wife and two children.
(Ms Turei lives in Dunedin, and Dr Norman lives in the capital.)
"I believe a co-leader should live here [Auckland] full time," Mr Hughes said.
He also hoped to help drive the party's vote across the 15 per cent line.
Mr Shaw, who has a background in business, named climate change as his number one priority but said the Greens also had to continue strengthening the economic credibility built up by Dr Norman.
The party needed to continue its growth and transformation into a body with a broad base, or face having the country's next government decided by New Zealand First leader Winston Peters, he said.
Mr Hague said he wanted the parliamentary party to gain the strength to deliver transformative economic and environmental changes.
Mr Tava, the only non-MP to run for co-leader - and the only contender to sport an Anzac Day poppy - said it was important the party identified with neither the left nor the right. He said issues of environment and social responsibility were not only for the left wing, and both needed to be considered to create an "integrated solution" to global warming.
The search for a male co-leader follows Dr Norman's decision in January to step down after almost a decade in the role. Party members will vote at the AGM on May 30 for his replacement. Ms Turei is the sole nominee for female co-leader.
Who's the man?
James Shaw, 42
•Born in Wellington. Entered Parliament last year.
•Before becoming an MP, he worked as a business consultant in London and here.
•In 1994, he co-founded the Republican Movement of Aotearoa New Zealand.
Vernon Tava, 37
•Born in Australia, but has lived in New Zealand for 26 years.
•Works as a lawyer and is a board member of anti-animal exploitation group Safe. •Member of the Waitemata Local Board and lives in Auckland Central.
Gareth Hughes, 33
From Gisborne.
•Greens' spokesman on energy, oceans, mining (oceans), information and communication technology, youth, and libraries and archives.
Has a degree in religious studies and history.
Kevin Hague, 55
•Born in England, lives in Greymouth.
•Greens' spokesman on ACC, alcohol and other drugs, health, housing, rainbow issues and sport and recreation.
•Has a bachelor of science degree in maths and geophysics.