A couple of things to remember:

• Even if UA has issued boarding passes for the NZ flights, NZ will issue new BPs at LAX. You can get the new BPs either at the check-in desk (premier check-in to the right in the CI area) or in the NZ lounge (unless NZ has managed to train the BP checkers at security to no longer allow UA BPs)
• If you've checked bags all the way through, make sure that the NZ staff enters the bag check ID in their system. They're usually very good at asking for your bag check slip, but they can occasionally forget. If the bag ID isn't entered, your bags will get an extended vacation at LAX...