I know that at 4:45pm the NZX goes into some weird state for 15 minutes before executing the orders that might match at 5:00. It's like a holding pattern; I think it's also ridiculous.
The ASX close at 4pm and go into a similar state for 15 minutes and then does a volume weighed auction which I quite like.
RE: ASB/ANZ. I went into ANZ bank today and asked them to print me a registration form for their securities - because I told ASB after their last round of incompetence that I had had enough. Yes it's not easy - and I don't know whether I can really be bothered with it. I pointed out to their staff that it's confusing that they have
https://www.anzshareandbondtrading.co.nz/ and
https://www.anzsecurities.co.nz both with different application forms. They were originally going to print me the first one before I told them the latter seemed the ticket.