I used to use I think skypark but found Air NZ had slightly better pricing. Tried another one previously but the experience was crap - basically some portable shed in the middle of a dirt/gravel area waiting in a line to sign in, and another place I thought the km were a bit high on my car so I made the switch to Air NZ and have been happy since. They do a great job of removing dog hair too! Cheaper than some other places. Cheaper petrol at the Waitomo? (W something) gas station just across the road from coming out of freight place. Don't think they do 95/8 though.
I think Air NZ own the service. They have a few storage sites. Can't remember how many parks but a lot! I recall talking to one of the drivers saying they initially bought another guy out who stayed on to help run it then NZ I think offered out the contract and someone else won it so they let the original guy go who then kicked the bucket soon after!
The place is running well I think. They updated the booking site this year which was good but I emailed them saying it would be nice to see the bookings especially since I forget what I've booked some times as I don't always book at the same time as flights and its tedious searching emails. Dropping off and pick up is pretty slick in comparison to my other experiences.
You can check in for domestic flights at the kiosks but they're still working towards international check in. Last did that in Oct.
The vans go around every 5-10min. I don't even bother calling when I arrive back, just come out and they're either there or arrive soon after.
I found NZ taxi's still somewhat expensive. I use it infrequently. The APD earn is outweighed by the taxi price. cheaptaxi.co.nz has some good fixed airport prices. Requires cash though and booking I'd say 24hr in advance as I've been turned down under that time frame saying "we're too busy". Uber I can pay via work cc with receipts emailed so sometimes good. Skybus sometimes too but pain in the backside now they go via Queen St. They used to stop just across from the ferry's which was great but now stop just down from Mercure on I think Customs st. Unpleasant if raining with bag. Used super shuttle previously but not since returning to Akl.
Obviously Akl specific answers.