An empire can become a subject either forcefully through wargoals or willingly, though the latter requires both a superior relative power and a positive attitude towards the superior party. If an empire becomes a subject willingly it brings a temporary +30 Opinion. If it becomes a subject forcefully it brings a temporary -30 Opinion
If they have fleets available, subject fleets tend to follow the overlord's.
The relative fleet power between an overlord and its subjects is always available regardless of intel level.
There are a number of types of subjects available depending on the overlord's government. Most of them have to pay a certain tribute to the overlord.
For subject empires the attitude is replaced by loyalty, expressing how content they are living under their Overlord’s rule. If a subject becomes disloyal they refuse any deal with the overlord and have a chance to start a war for independence, always waiting for an opportunity when something depletes the overlord's relative power (a taxing war, a larger uprising, a crisis, etc.). The loyalty is determined by the subject's opinion of the Overlord, which aside from the normal factors is also affected by the total military strength of all the subjects relative to the Overlord as well as that of those who support their independence.
An Empire is able to support the independence of another Empire's vassal. Doing this will count the supporting empire's fleet for the "relative power of subjects" opinion modifier, causing the subject to rebel if they stand a good chance of victory. If they do, the Empire supporting them automatically joins their war for independence.
Subject empires do not suffer from border friction and can therefore in some cases be utilized as buffer states between two empires that otherwise would have significant border friction issues.
Vassals and Protectorates that an empire possess for longer than 3 600 days can be peacefully "integrated" by paying influence, at a rate of 5 influence a month. The base cost is 50, increased by 1 for each pop and 10 for each planet. Empires with the Shared Destiny ascension perk benefit from a -50% influence cost to integrating subjects. Only one subject can be integrated at a time.
Once the integration is completed, all planets and ships of the subject are transferred to the overlord; the ships and starbases retain their graphic type. All leaders, resources and armies are removed; new scientists are required for their science ships.
Releasing as a vassal
A player can create a vassal from their own territory by releasing one of their sectors as a vassal from the "Sectors" tab by clicking the "Create Vassal" button next to the sector they want to release. The player can then transfer additional systems to their vassal through the Trade option "Transfer System" if they so choose. Sometimes it is preferable to conquer systems and then release them as a vassal since this will create a vassal that shares the overlord's ethics and government. Notably, the vassal will be granted all its overlord's technology. The option to release a vassal is not available to Machine Intelligences (except when you have no robot pops in the sector), Genocidal empires, species with Stellar Culture Shock, or the Hive-Minded and Nerve Stapled traits.