I’m an Australian citizen or an Australian permanent resident, am I eligible for fees-free study?

Yes, as long as you have lived in New Zealand for three years or more while holding a residence class visa and you meet the other eligibility requirements.

You don’t have to have lived in New Zealand for three years in a row, but you do need to have lived in New Zealand for three years in total while holding a residence class visa. If you haven’t lived in New Zealand for at least three years you still qualify as domestic students for tuition subsidies and regulated student fees.