A holding represents a controlling stake in the industry or economy of a particular territory that can be owned by a particular character, usually a head of family, giving them considerable influence over the area. Holdings provide income and power base to their owner, and can be viewed in the Holdings mapmode.
Except for the country capital, each territory has one holding slot which can have a single holding owned by a particular character. There is no limit on the number of holdings a character can have.
Every holding gives power base proportional to the total number of territories in the country, irrespective of its wealth or population. A character will get +0.5 power base for every percentage of the country's territories it controls as holdings (alternatively, all territories together - including territories without held holdings - are worth 50 power base in total, with power base from holdings determined how what proportion of the country's territories the character owns as holdings). For instance, if a character owns 10 holdings in a country with 21 territories, they will get 23.81 power base from their holdings.
Holdings in territories with an empty holding slot can be granted to a head of family using the Grant Holding interaction at a cost of 40 gold. The beneficiary will gain 5 loyalty, decreasing at a rate of −1 per year. If the beneficiary is the ruler, an additional cost of 5 ruler corruption will apply.
Heads of family can buy holdings in territories with an empty holding slot using their personal wealth with the Buy Holding scheme. With this scheme, characters will always prefer to buy holdings that are adjacent to currently held holdings. Characters that are not heads of families usually do not have holdings of their own, but can sometimes earn them via plots or events.
When a head of family dies, all their holdings will be inherited by their successor as head of family; if a non-family head character dies, their holdings are inherited by the head of their family. These means that holdings, with the wealth and influence that they entail, will almost always be concentrated among the heads of family.
A holding can be revoked from a head of family with the Revoke Holding interaction at a cost of −5 loyalty, decreasing at a rate of +2 per year. Holdings with the Family Estate modifier cannot be revoked normally. This can be used to slowly reduce the power of a family by slowly revoking their holdings at a rate that does not anger them too much, but in larger countries where each individual holding matters less revoking will generally become less useful over time.
If the country has at least 40 tyranny and the head of a great family is imprisoned, they can be proscribed at a cost of a further 30 tyranny. Proscription will revoke all of family head's holdings, including those with the Family Estate modifier, execute the head, and demote the entire family down to minor character status with a loyalty penalty of -40. This extreme option can be used to completely destroy the power of a dangerously powerful family, but is highly costly in terms of and requires imprisoning the head, which can itself be risky if a trial is needed.
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Holdings are important in the balance of power between the great families of your empire. If left unchecked, the heads of great families could try to buy more and more holdings to snowball wealth and power base. Mark the heads of great families to keep track of their activities, and find opportunities to revoke holdings; befriend them for increased loyalty.
You should be careful when you grant a holding to your ruler because of the corruption; if removing the corruption is critical, remember that setting wages to High (in the Economy tab) will remove the 5 corruption in 50 months (as well as remove the same amount from your officials and governors). Also, note that while every holding grants the same amount of power base, their income is highly variable according to the wealth of their territory. So if you play a monarchy, try to preempt big cities and highly productive territories. If you play a republic or a tribe, try to preserve equilibrium between the families since the ruling family will change at one point or another.
If a family becomes too powerful, you can revoke their holdings to try to contain them. If the situation becomes really serious, you can bring the head of family to a trial to imprison and proscribe him. But be aware that if you lose the trial, a civil war might occur.