An Australian resident or citizen will have to pay CGT to the...

An Australian resident or citizen will have to pay CGT to the ATO. A New Zealand citizen resident in NZ (i.e. me) does not pay CGT on Australian or NZ share transactions. However, the NZ Tax Office takes 30% of all Australian-earned dividends as provisional tax, this is deducted by the broker at the time of the dividend being paid and sent directly to the NZ Inland Revenue Department (Tax Office).
Better for me to sell shares pre-div and buy them back post-div at the (usually) lower price, even though this does involve two lots of broker commission. If you are very smart or lucky you can earn more with the Capital Gain than you lose by taking the div less provisional tax.