New Zealand Law
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The Status of Children Act does say that you are not the parent in this situation, as you were not the woman's partner at the time of the birth or subsequently, and so you do not have the rights under the Care of Children Act as to contact with the children.
As you are aware the agreement is not recognised by the legislation, and so your only way to get contact other than by consent, would be to apply to become a guardian under the Care of Children Act.
There have been some lawyers who have written about these issues, but I would suggest some senior in this situation, like Simon Jefferson in Auckland. His contact is http://trinitychambers.co.nz/simon-jefferson/