Province

A Province is an entity that can have industries and POPs. They are centered on being the simulation unit for economical aspects, this is, industries and POPs only work in Provinces and not nations or tiles.

Unlike countries, a province can only have only one unique colour, this is because the game engine will associate the province to the given province map which will detail the shape of the province itself. Black (0x000000) and White (0xffffff) colours are reserved by convention for marking sea and land respectively. However mods can use any colour they want since the game engine ignores any colour that is not associated to a province.

Changing owner
This function also updates the respective tiles in the map:

Obtain the owner
Another version of this function exists, this is for obtaining the controller of a province; which is the nation who owns most of the tiles in a province (but by treaty does not have it). For example a province from Prussia conquered by Russia, but while Prussia is still at war, will return Russia since it is the current province controller.

Give to
Will give up a specified province to another nation; does not affect buildings or units inside said province.

Give and relinquish
Since 2.9.9 a province can be given AND relinquish all the property within said province (best case use would be, ex. a "unify all" event for a country). The difference from a normal give_to is that this one will give up all the units and buildings located in said province from the original owner.

Set terrain
Provinces need a defined terrain type for them to function properly (they will, by default, use the TerrainType with an Id of 0).

Obtain neighbours
A province has their neighbours be automatically generated at the start of the game; they are somewhat "permanent" in respect to the province for the length of the playtrough.