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Three-year-old Qian Xun Xue remains in foster care after she was left at Southern Cross Railway Station by her father, Michael Xue, on Saturday.
He is now a suspect in the murder of the girl's mother, 27-year-old Annie Liu, whose body was found in the boot of a car outside the family home in Auckland.
A post-mortem examination revealed she died from what has been described as an unspecified violent episode.
New Zealand Immigration Minister Clayton Cosgrove told ABC Radio's PM the girl's grandmother, 53-year-old Liu Xiaoping, has been given permission to go to New Zealand.
"We have prepared all necessary documentation, I have waved a large number of requirements and there is now no impediment for the grandmother and her people from travelling," he said.
"My latest advice is that they are in the process of confirming travel arrangements to New Zealand.
"It's likely that once she arrives in New Zealand both our social services will go through the care and protection process which will be expedited and then we will seek to reunify as swiftly as possible."
Half-sister
The half-sister of Qian Xun Xue says she was also abandoned by Mr Xue.
Grace Xue is estranged from her father and was reported missing five years ago, but she contacted police this week.
She has told TVNZ her father left her two months after they moved to New Zealand, and she is worried about the little girl.
"What is going to happen to her, is she going to be looked after and is she going to go through the same emotions as I did when I was little?" she said.
"What can I do to help her not to feel the same way."
She says she has never met her half sister, but told TVNZ her father is a selfish man who also left her when she was young.
"I actively try not to think of him. What I would say to him? How could you, she is just a little girl," she said.
"I am angry, but I am more sad."
Complex investigation
Meanwhile, senior New Zealand police officials have strongly defended the handling of the investigation in what is now being referred to as the "body-in-the-boot" case.
New Zealand police are smarting from criticism by the public and retired police officers that their handling of the inquiries into the abduction the toddler and the murder of her mother had been bungled.
Deputy Commissioner Rob Pope says relevant international law enforcement agencies were alerted as soon as the child's identity was confirmed and standard forensic protocols were observed in the search for her mother.
"For anyone who steps back and looks at the complexity of what they are dealing with I think they'd be struggling to put the term keystone, unprofessional or slipshod to this investigation," he said.
Police have established that Ms Liu made her last phone and email contact with family and friends on September 10, four days before her estranged husband Michael Xue left New Zealand for Melbourne and then Los Angeles.
Police have issued a warrant for his arrest for the murder of his wife and the abduction of their daughter, and say they are now liaising with Interpol, the FBI and the US Marshall Service to find him. © 2007 Australian Broadcasting Corporation