I’ve flown Auckland – Los Angeles – London and back several times and all I have needed is an ESTA: https://esta.cbp.dhs.gov/esta/.

The transit time is only a couple of hours and most times I have had to clear immigration, collect my bags and return to the check in desk. This would have meant that I could have just walked out of the airport and gone where ever. I just put on my arrivals card that I was in transit.