How do I close a New Zealand company that has stopped trading?

Apply to remove it from the register. You need a shareholders' special resolution, where required, and a no-objection letter from Inland Revenue. The Companies Office then publishes a notice, and if nobody objects within 20 working days the company is removed. A company with debts it cannot pay goes into liquidation instead.

Company closure

Source: Applying to remove your company from the register, New Zealand Companies Office