it wouldn't exactly be HECs per se. It wouldn't be through tax.
AFAIK, the nominal amount of loan (through handful of authorised schools) is interest free while in NZ and only accrues interest when outside country. I'm sure there's plenty official info out there.
One has to be NZ resident or citizen. No idea how it works for Australians who have right to work there, but won't be full residents de iure according to NZ immigration law. I'm sure it would be matter of few thousand NZD for paperwork if you're in skilled employment with some experience.
The same idea as when OZ does not grant social benefits entitlement to Kiwis heading over, unless they sort proper residence visa or citizenship..
D&G subforum should have more info if you can't find any relevant stuff via google. Those big schools do list the option of getting student loan on their websites if they have that option.