There are a few very good links if you suspect your people came to New Zealand via Australia and were assisted passengers or their parents were.
The NSW search page.
The VIC search portal. (Prov guide).
Then today Shauna Hicks, Australian genealogist and family historian, archivist, researcher, speaker, writer, and traveller, tweeted that there was an online reel of assisted passenger lists for us to see. Wow! The power of the internet. If you are lucky and have passengers on one of these ships, you can get some useful information.
The ships list for this reel.
About the project.