Overstayer Geeta Praveen Samujh is fighting to stay in New Zealand to be with her month-old son, who is a New Zealand citizen by birth because his father is a permanent resident.

Immigration New Zealand has sent a letter to Ms Samujh encouraging her to depart the country voluntarily because she has been in New Zealand unlawfully for two years and 10 months.

Changes to the Immigration Act next month will mean the service can manage overstayers quite differently and, depending on circumstances, may even detain some in secure detention or require them to report regularly.

"Immigration New Zealand has not served a removal order on Ms Samujh. She has been sent a letter advising her of her status and that she should make arrangements to leave New Zealand as soon as possible," said Nigel Bickle, Head of Immigration.

"She has also been provided with the contact details of a compliance officer if she needs to discuss her options."

Mr Bickle said it cost the agency an average of $2450 for a person to be deported.

Ms Samujh, 37, first came to New Zealand from Fiji as a student in 1992 on a New Zealand Vice-Chancellors' Committee scholarship and then again on a work permit in 2006, which was revoked when it was discovered that she had ceased working for her employer without notifying the service.

She gave birth to a baby boy - who she has not yet named - last month but has since separated from her son's father, who is a resident.

"I have to be in New Zealand with my son who has a health condition and it is not possible for me to take him back with me if I am deported," Ms Samujh said.

"I do not have any family in Fiji and have lived in New Zealand for nine years.

"In accordance with principles of natural justice and fairness, I should be allowed to stay with my son as he needs me."

Immigration New Zealand says it has been advised by Ms Samujh that she has a child who is a New Zealand citizen but she has not provided a birth certificate.

"If the decision is made to remove a person from New Zealand, the care of any New Zealand citizen children is the responsibility of the parents," the agency said.

(Source Lincoln Tan, NZ Herald)