The thrust of NZ republicanism seems to be a little different from its Australian counterpart, at least according to the the Republican Movement of Aotearoa New Zealand:
We believe that a New Zealander should be our head of state. They should be elected democratically and be accountable to all New Zealanders. These ideas are the heart of republicanism – where power comes from the people.
Note that the focus is very much on democracy and accountability, a more radical position than that taken by the ARM, who focus almost exclusively on the need for an Australian as a head of state. No doubt this is a legacy from the Referedum on '99, and in line with the ARM's non-commitment to a particular model. It seems, however, that the RMANZ might be making the same mistake as the ARM did the first time around.