I sailed in Union Co ships in Australia from 1968 to 1976. My ships were:- Poolta, Pateena, Koonya, Kumalla, Kootara, Seaway King, Seaway Queen, Seaway Prince and Seaway Princess as well as Abel Tasman when it was taken over from HC Sleigh. As you can see this list of names is a little at odds with flyer682's note about maori names.
Further to Chris Field's note on the fleet size, I have in front of me the Passenger List for Aorangi - Voyage 72N, sailing Sydney June 1, 1950. This booklet lists 7 passenger vessels (one building - Tofua), 59 cargo vessels (6 building - Kawaroa, Kurutai, Karoon, Kootara, Kawatiri & Kokiri), as well as Aorangi herself of Canadian Australasian Line and Taroona of Tasmanian Steamers. I don't know about the various NZ coastal lines, but even without them 68 ships is a pretty big fleet.