I post in the hope of the collective wisdom giving me a clue. I have deliberately used gender neutral terms. I do NOT want this to degenerate into a slanging match over gender based issues. The background is real, and very sad. If there is a detail missing please ask.

Parent 1 is a US citizen who has lived in NZ for some years.
Parent 2 is a NZ citizen.

They met overseas and decided to live in NZ.

After several years they had a child. (Born in NZ)
The relationship has failed.

They have a sort of shared care arrangement. Neither will put anything into writing!
Parent 1 has gone on DPB with the consequential CS liability on parent 2.

The questions arising,
Parent 1 is off back to the US. Do they forego DPB? (It is an open ended visit)?
If they forego DPB does this inturn relieve parent 2 from the (NZ) CS liability?

Is there any consequent liability from the US?

If in the mean time parent 2 heads to Australia to work What happens to the liability for CS?

All comments needed, they will affect decisions.

Thanks folks.