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Shane William Grogan, also known as Shane Calder, is alleged to have befriended at least three women through internet sites, then stolen from them.
The 46-year-old from Christchurch travelled to Rotorua last October to stay with a woman in her 50s who he had met online, police claim.
They say he left abruptly, taking a bankcard he used to withdraw money, and a car which was later recovered.
Police allege that the following month Grogan travelled to the Palmerston North area to meet another online contact, a woman in her 30s.
He stayed at her home for a week, and proposed to her before leaving abruptly with cash and other belongings, police say.
The latest allegations concern an incident police say occurred around New Year when Grogan travelled to Waimate to meet another woman in her 50s.
He stayed with her for six days but left after stealing valuable heirloom jewellery and a computer, police allege.
Officers claim Grogan returned to Christchurch and pawned some of the stolen items. Some of the stolen jewellery has now been recovered.
Acting Sergeant Chris Macpherson says the alleged offending was deceptive and predatory and it's possible other women may have similar incidents to report.
Grogan is wanted on warrants in relation to charges of theft from a dwelling, using a document for pecuniary advantage and unlawfully taking a motor vehicle.
He is described as European, 1.9 metres tall and of thin build.
Mr Macpherson says the allegations should serve as a warning on the dangers of befriending strangers through internet sites.
"We always urge people to be cautious about people they meet online and not rush into relationships before they are certain of their character and intentions."
Anyone with information on Grogan's whereabouts is asked to contact Christchurch police on 03 363 7400 or Crimestoppers, anonymously, on 0800 555 111.
- By Kurt Bayer of APNZ