Most Council operated cemeteries are lawn cemeteries where the headstone is placed on an existing concrete beam at the head of the grave. Cemetery by-laws dictate the base and headstone dimensions, particularly the height of the headstone. As a guide, the most common size for an up-right lawn headstone is 700mmx550mmx75mm on a base measuring 915mm (width) x450mm (depth) x100mm (height). There is a by-law guide to memorial sizes etc, but each controlling council has its own specifications.
Granite is the preferred material in most cemeteries. A permit is required before any memorial is erected in a Council cemetery. Private and urapa cemeteries are not governed by the same rules as apply above so generally you are able to put in any size and base that fits the plot.
Hawkes Bay Council links:
CENTRAL HAWKES BAY: https://www.chbdc.govt.nz/services/cemeteries/cemetery-database/