I hired a freelancer to design my logo, do I own it?

You may not own the copyright. Under the Copyright Act 1994, the author of a work is usually the first owner, and unlike some countries, in New Zealand a person who commissions a work does not automatically own the copyright, unless there is an agreement. If there was no written assignment, you may only have an implied licence to use the logo for its intended purpose, which may not be enough for exclusive rights or a trade mark application. The solution is to ask the designer to sign a written assignment of copyright, which must be in writing and signed by the owner to be effective, and to include a waiver of moral rights if appropriate. Approach it in a friendly way and offer reasonable payment if needed. Use written contracts for future creative work.