To be clear, then we're talking here about state pensions only, and any private pension funds are excluded from this? Ie any NZ held or UK held private pensions would not effect the pension paid in NZ?
Whilst it may be a nasty surprise, then the BASIC pension is actually more a benefit to ensure that everyone has a base income that allows them to survive in their old age. Private pensions that people have contributed to outside of any basic state scheme are to allow people to retire with a higher income / standard of life. My reading of the above is that these private pots, wherever in the world they are based aren't included in the calculation.
What has not been discussed here I don't think is eassae's question about how pension contributions made in NZ would apply to someone who is overseas when they retire. I'm guessing that due to the many diffferent schemes, and the policies for each potential 'end' country, then that's more likely to be something that you need to seek specialist individual advice on.