An important point. I booked a BA ticket from LHR-AKL-LHR some years ago with a change each way at LAX. Sure enough, BA screwed up on the LHR-LAX sector and I missed my connection which was to be flown by Qantas. When I tried to sort things out on the ground, BA couldn’t have been less helpful but fortunately, Qantas put me on a flight leaving two hours later, so it all worked out in the end.