At any one time between June 1942 and mid-1944 there were between 15,000 and 45,000 American servicemen in camp in New Zealand.
Given that NZ's total population was only 1.6 million at that time, this was a significant event in NZ history. The U.S. used NZ for both rest and relaxation for their troops from the Pacific War and also as a staging post for operations. Hospitals were built (in joint cooperation between U.S. military and NZ govt.) with facilities for approx. 10,000 patients. Some female nursing staff was brought out from the U.S. to help staff these 19 hospitals.
Over the years I have spoken to many women who remembered the American troops in NZ. It was an exciting time in many ways. The American presence helped New Zealanders feel more secure about any potential Japanese invasion. With the shortage of kiwi men on home soil, there were many relationships formed, broken hearts, babies born, etc.
This era is affectionately called "the American invasion" of NZ.
This old movie clip has footage of the first American troops arriving in NZ.