Ownership
A country's ownership of a province is a claim to the province that is recognized by other countries. Every province with a trading post, colony, or city is always owned by some country. A province is unowned (or empty) when it has no trading post, colony, or city.
Ownership of any empty province may be created by colonization. Province ownership can be transferred from one country to another via a formal peace treaty, and a few other circumstances. It is generally not possible to "disown" most provinces; however, it is possible to burn enemy trading posts, making the province unowned. It is also possible for natives to destroy trading posts and colonies, again resulting in an unowned province.
Control
Ownership of a province is distinct from control of it. An enemy army will take control of an unfortified province merely by entering it, if no battle is offered. If a friendly army is present, the enemy must win the battle to take control. It is not as easy to assume control of a fortified city: to take control, an enemy must siege it to the point where it surrenders.
When a country has control, but not ownership, of a province, the province is occupied. Occupied provinces have a small malus to population growth. Control of the province gives some use of it to the controlling country; if it has a port, it can be used, and the supply afforded goes up somewhat. However, controlling a province is very different than owning it.
One exception to the control/ownership distinction is that offered by the Treaty of Tordesillas. While it is operative, Spain and Portugal may take ownership of any province owned by any Catholic country within the ToT area simply by taking control of it. Furthermore, they don't need a declared war to take control or even to siege.
Transfer of Ownership
In general, province ownership is transferred only as a result of a peace treaty concluding a war. When proposing peace, a country may ask for any of the enemy's provinces which it controls, as well as any of its own core provinces (regardless of control). If the enemy country agrees to the treaty, province ownership is immediately transferred.
Other circumstances of ownership transfer are these:
- Diplomatic annexation
- Defection
- Government collapse
- Revolt
- Inheritance events (rare)
- Cessation and independence events (very rare)
- Releasing a vassal
- Spain or Portugal taking a province via Treaty of Tordesillas rules.
Whenever provinces change ownership, any existing tax collectors and/or chief judges are removed. Any projects ongoing in the province are terminated. Also, when ownership of a city changes via most means, the city will suffer from nationalism for a while. (Defection is the exception here. Revolting countries and freed vassals do not experience nationalism, but that is because they only get core provinces and no country has nationalism in its core.)