I have a family member who recently entered in a relationship with an New Zealand national?

If she can meet the requirements to be considered the New Zealand citizen's partner, she could then apply for a visa under the Family Partnership category. She must prove that they have been living together for at least 12 months in a genuine married or de facto relationship and the NZ partner must support her application. Simply being pregnant to a NZ citizen isn't NEARLY enough for her to be able to stay.

http://www.immigration.govt.nz/migrant/stream/live... Residence under the Family Partnership Category.

Committing procreation is not any qualification for any visa, immigration, or anything else. Poor planning - outright carelessness on her part - does not constitute an emergency on anyone else's part.

She needs to return to her own country & arrange for either an abortion, adoption, or raising a child on her own. Obviously, he has no intentions of marrying her or that would have transpired. In fact, premature procreation busts up more relationships than anything else.

Tell your family member, having a child does not allow them to break immigration laws. No country will allow a person to remain simply because they are going to have a child. If that were the case, every country would be flooded with bogus immigration claims. She needs to obey the order to leave or she risks being deported with no chance of returning.

You are correct, procreating doesn't get her a visa to remain