A satellite state, also known as a puppet, Sub-state, dominion or vassal, is a country which allows another nation to represent it on the international stage. The satellite state remains independent in terms of government, economics, and other internal affairs, but may not sign treaties or declare war on foreign countries. The "mother country" retains special privileges, being able to sign defensive alliances and military access treaties with the vassal state. It can also colonize in adjacent states. The overlord has a special diplomatic interaction to take control of the puppet's troops while at war.
If the mother country is at war then the satellite(s) or dominion(s) will automatically be at war with the enemy too (except if the enemy of the war is the sphere leader of the satellite).
The formation of master-puppet relations
Formation
A puppet-master relationship can be formed in two ways:
- A nation can force another nation to be a puppet state by war.
- A puppet state can be formed by releasing a nation peacefully.
Cancelling
A puppet-master relationship can be cancelled in five ways:
- The master nation ceases to exist, while the puppet continues to exist.
- A revolution in either of the countries happen.
- The puppet rises to great power status
- A cancel puppet casus belli.
- Certain events and decisions.
Other than attempting to rise to great power status, there is actually nothing a puppet can actively do to break free.
Spheres and puppets
However, great powers can still attempt to place the satellite state within their sphere of influence or, if the satellite's government allows it, invest in the local economy. The mother country (if a Great Power) receives 100% bonus influence with its satellites.
Formable countries can still be formed by influencing a puppet nation even if the forming nation is not the liege. This can be used to "steal" other nations' puppets by forming countries. The liege cannot do anything to prevent the formation. This is typical for 
North German Federation and 
Holstein. If one intends to form a country where one's puppet is needed, is it NOT enough to be the liege. The only way is putting it in one's sphere of influence.
Special Types of Satellites
Dominions
Dominions are countries that are released from colonial regions. A dominion gets ownership of and cores on all colonies and protectorates in a contiguous area, one of which becomes the capital and gives it its name and primary culture (it also accepts its overlord's primary and accepted cultures). It is civilized and has its overlord's technology and government type, but no reforms. The colonial points that the overlord was spending on upkeep are refunded. Dominions are therefore useful to free up colonial power for colonial competition and allow factories to be built in colonial areas (though since they tend to have low literacy, factories will not be very productive).
China
China starts with its own special kind of satellites called substates. They act as very loyal puppets as long as China is an uncivilized nation and will be inherited after China westernizes. They join wars that China enters as an ally, and provide military access to both sides. That is however not the case during the civil war between China and 
Heavenly Kingdom. The substates include 
Yunnan and 
Qinghai. If the substate westernizes before China, it will automatically break free.