You can apply to live in New Zealand permanently if you have a child who is a New Zealand citizen or resident. They must earn enough money and agree to sponsor you. You must submit an Expression of Interest and Immigration New Zealand must invite you to apply for Residence.
You must complete an Expression of Interest and receive an Invitation to Apply from Immigration New Zealand. There is an annual quota of 2500 places under this category.
You must meet health and character requirements for residence
You must be able to speak English
Your New Zealand child must meet an income threshold to be able to sponsor you
You must have no dependent children
Your sponsoring child must be a New Zealand citizen or resident and be living in New Zealand
You must be the parent or legal guardian of your sponsor