Causes of Inheritance
Inheritance is only possible via scripted events. There are no random events for it. Although there are sometimes in-game triggers for particular inheritance events (i.e., the Ottoman Empire can inherit Mameluks by taking control of Egypt after 1510), some inheritances are triggered by things outside of player control, i.e. actions selected by AI countries.
Resolution of Inheritance
When an inheritance event happens, the inheriting country takes ownership of all provinces owned and controlled by the inherited country. However, any province owned by the inherited country which is controlled by a third country goes to that country, not the inheriting country. As with other forms of annexation, the inheriting country gets all military forces of the inherited country, and all other assets related to that country vanish.
Inheritance is one of the few methods of province transfer that costs less than one badboy per province. The inheriting country pays 1/4 BB per province, regardless of which country gets the province.
Note that it is possible to exploit many inheritance events if you know about them ahead of time (by reading events files or paying attention in previous games). This is not possible in well-designed inheritance events, which restrict inheritances to peacetime. (Most of the events in most mods are restricted.) But if an event can happen in wartime, you can exploit it with any country in range. You invade the country to be inherited ahead of time, taking control of any/all provinces which you want. Then the inheritance triggers and you get them, BB-free.
List of Inheritance Events
For your exploiting pleasure, here is a list of inheritance events that can happen in vanilla EU2 1.09. The "probability" field gives, roughly, the probability that AIs will select option in events such that an inheritance happens.
|1451||89.4%||Provence||France||Exists FRA, ENG|
|1451||89.4%||Luxembourg||Burgundy||Exists FRA, HAB, !War|
|1470-||100%||Aztec||Spain||Until 1560. Must control Zacatecas|
|1476||94.4%||Burgundy||Austria||Exists FRA, HAB, !War|
|1476||5.6%||Burgundy||France||Exists FRA, HAB, !War|
|1500||89.4%||Milano||Austria||Exists FRA, HAB|
|1500||5.3%||Milano||France||Exists FRA, HAB|
|1516-||100%||Hungary||Austria||if OE holds 3 Magyar cores|
|1540||100%||Hungary||Austria||if 1516 event never happened|
|1559-||100%||Gelre||Holland||as soon as HOL exists|
|1559-||100%||Friesland||Holland||as soon as HOL exists|
|1559-||100%||Flandres||Holland||as soon as HOL exists|
|1559-||100%||Brabant||Holland||as soon as HOL exists|
|1589||100%||French Protestant Rep.||France|
|1637||5.3%||Pommern||Brandenburg||Vorpommern to Sweden|
|1649||100%||English Royalists||England||Only if ECW happened (1642), went PUR|
|1649||100%||English Puritans||England||Only if ECW happened (1642), went ROY|
|1688||100%||PUR||England||If Restoration happened (1660), went ROY|