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Is your LHR-AKL flight via LAX or via HKG? If it is via LAX then piece baggage allowance applies, if via HKG the weight baggage allowance applies.

Since it is all on one ticket the same type of allowance applies for the entire trip. However, individual airlines' policies can affect what you can bring.

If the piece allowance applies then you have 2 pieces. NZ limits each piece to 23kg. SAS limits each piece to 23kg also.

If the weight allowance applies then you have 20kg total allowance, and this applies for both airlines.

If you have star alliance gold (*G) status or are flying in business class then allowances are higher.

If you were flying SAS CPH-LHR on a ticket that does not include North America then the 20kg allowance applies. This may be where there is confusion.