The Kiwis, a bunch of violence-obsessed psychopaths if there ever was one, ?
LOL

- you must have met some of the guys I used to drink with at the local, "The Flying Jug", in Cannons Creek (Porirua).
.... kept their single division in the Med (Italy) once war broke out in the Pacific.
WI if it had been bought back to the Pacific? How would/could that happen?
Where would it have fought, what would it have done? Would they have been ANZACed? Would they have made much difference?
How? well, the Aussies brought their Division back from the ME because they were shit-scared of a Japanese invasion and Churchill left them hung out to dry. The fall of Singapore, the Phillipines and the Dutch East Indies might be said to have caused the Aussies and Kiwis "some concern." NZ was just a little further away and not as directly threatened and so left the Div in the ME. Also, the US sent a Marine Division to NZ (they trained and had their camp a few miles from where I grew up, just outside Paekaekariki - pronounced and shortened to "Pie-cock" for those who have no idea how to say that) so NZ wasn't quite so much at risk.
BUT perhaps a direct request from the Aussies to bring back the NZ Div to help with the defence of Australia? With enough pressure from our friends in OZ, NZ might well have xferred the 2nd NZ Division back.
Would they have been ANZACed? Maybe, depends where they fought, with the Aussies or with the Yanks. If they'd arrived back at Aussie request, more than likely they'd have been thrown into New Guinea which would definitely have resulted in ANZACing them.
As it was, NZ did form the 3rd Division in 1942, it fought in the Solomons during 1943–44, but was disbanded in October 1944 (the majority of its manpower was returned to civilian employment, although around 4,000 men were sent to Italy as reinforcements for the 2nd Division). In early 1944 the New Zealand Government faced a manpower crisis caused by the demands of maintaining two divisions overseas while simultaneously maintaining agricultural and industrial production to meet the needs of the Allied countries. In order to cope with this crisis the NZ Government saw no option other than to disband one the country's two infantry divisions
(The 1st, 4th and 5th NZ Divisions were Home Defence formations, the 2nd and 3rd Divisions were the "expeditionary force" divisions and a fake "6th NZ Division" was created in Egypt in 1942 as a deception formation. There was also a 1st NZ Army Tank Brigade" but this was fairly short-lived. There was never enough manpower to bring the 3rd Divison up to full strength.