Mr Tremain was born in 1941 and became a professional painter in 1972 and a cartoonist in 1988.
He died on Saturday in Lakes District Hospital in Queenstown.
Visual artist Sir Grahame Sydney said he had known Mr Tremain for more than 40 years and he was "wonderful company".
"He was very sharp, very intelligent, very witty and very unafraid and highly opinionated."
Sir Grahame believed Mr Tremain was the best cartoonist in New Zealand for the decades he was active.
"A great many people looked forward every day to seeing what Tremain had to say in his cartoons, and they rated him very highly indeed."
It would not be an exaggeration to say he was the successor to the famous New Zealand cartoonist Sir David Low, Sir Grahame said.
Mr Tremain attended Palmerston North Boys’ High School.
He moved to Queenstown to become a landscape painter and he lived there with his wife, Jill, until she died last year.
Sir Grahame said Mr Tremain only took on cartooning when he discovered he could fax his illustrations to publishers from his home.
A lot of his work was political satire, and he published daily cartoons for the ODT until 2019 when his tenure ended amid controversy.
In October this year, he launched his autobiography This Is It Then in Arrowtown.
— Allied Media
