New Zealand was a vital part of the supply line to the European and Pacific theaters. The Japanese advance on the Solomon islands was, in part, to break that. From the north they got as far as PNG. VERY close to Northern Australia. There was a big schintk about it. Aussie troops were pulled home to fight the advancing Japanese off against Churchill's instance that they stay in North Africa to fight the Germans. After the bombing of Darwin it all changed. Lots of reading on that subject. Kokoda is a pretty good film if you want a quick history lesson.
New Zealand troops stayed in the Mediterranean and North Africa while the RNZAF went off to fight in the Pacific. At its height we had 28 (IIRC) squadrons based in the Pacific. The top Allied ace was Geoff Fiskin, a Kiwi. In fact, if "The Pacific" is historically accurate the two Kitty Hawks in one of the early episodes would most likely have been RNZAF based in the Solomons. My Granddad wound up in Scotland serving with the RNZAF, his records make for some interesting reading.
My Great Uncle was in the Div Cav, served in North Africa and Italy. He was awarded the MM at Anzio. The Kiwis pulled the Yanks fat out of the fire there. Oddly enough, the local Italians no more about Kiwi involvement than most Kiwi's. Sad really. Anyway, I got some info off the NZ archives as my Poppa always told fish stories. Seems the one about his brother was true.
I could go on for hours. I started reading up on Kiwi's a couple of years ago. There is plenty that has been forgotten, and a lot not recounted accurately. I would have loved to be an Archeologist. Have a read of this, uncle (Lance Sergeant) Fred's MM citation;

This was across the Rapido River. One hell of a scrap.