The Courts of Chaos are effectively a feudal state. The vast majority of the population owes allegiance to some lord, who himself owes allegiance to some greater lord, in a pyramid ultimately capped by the King himself. Vassals grant some sort of service to their Lord, in return for the Lord's protection and assistance in times of need. This service may be military, financial, labor, intellectual, or many other different forms. Lords sometimes also grant land or entire shadows to their vassals, especially at the higher reaches of the Chaos hiearchy.
Thirteen Great Lords and Nine Free Cities give their allegiance directly to the King of Chaos (in theory), and form the top of the Pyramid of allegiances. Some of the Lesser Houses have at times also given direct allegiance to the King.
The Great Lords are descended from the thirteen sons and daughters of King Dios. The Nine Free Cities are shadows chartered by the King of Chaos with special rites and privileges. The Lesser Houses were founded by the King or by the Great Lords to reward faithful followers.
The King of Chaos holds his position by right of descent from King Dios, founder of the Kingdom of Chaos. The current king, Ishmael, is in fact the eldest son of King Dios, and has ruled for hundreds of years now. He seems unlikely to die any time soon, either.
The Chaosian succession is a complex issue; King Dios created an elaborate system by which to measure closeness of descent from himself; in theory, whoever is closest in descent to King Dios is the heir to the throne at any given time. The intermarriages of the Great Houses have helped to make this rather complex.
While Chaos has a King, his power is not absolute. Each of the Great Houses possesses extensive powers over their own lands which the King cannot override, and the Lesser Houses and the Nine Free Cities possess some degree of autonomy as well. His ability to coerce the Great Houses, or even the Lesser Houses into action is dependent on his building a strong enough base of support among the other houses to be in a position to do so.
Two major institutional checks on Royal Authority exist. The Great Council is made up of the thirteen Great Lords; the King himself sits as permanent chairman of the Great Council by dint of his being King. No direct levy on the Great Houses can be made without its approval, its members can only be tried for treason by the other members and cannot be punished for any lesser crime, and it must approve any declaration of war or peace by the Courts as a whole. Each member designates a representative who sits on the so-called 'Council of Feuds', which regulates the declaration of Private Wars by greater and lesser houses alike.
The Senate of Chaos is the second major check. Every Great House sends three representatives; every Lesser House sends one representative, chosen by whatever method they like. The Nine Free Cities each send two representatives, and the Courts of Chaos proper sends five. The Royal Chamberlain, the Royal Marshal, the three High Judges, and the Royal Treasurer also hold seats in the Senate by virtue of their office. All Royal Laws must be approved by the Senate (and by the King). The same applies to repealing laws. While the Senate has no theoretical power to make war and peace, in practice, a war unsupported by the Senate will tend to be conducted rather weakly. The Senate has no power over royal appointments, but can 'impeach' royal officials, forcing them to be fired in disgrace.
The Great Houses, the Lesser Houses, and the Nine Free Cities all possess a great deal of autonomy; only the Royal Desmene, which forms effectively the so-called 'Fourteenth House' is under direct, total Royal Control.
The King can appoint anyone he likes to hold royal offices. He can spend his income however he likes. He can issue royal edicts which hold the force of law over the Royal Desmene. The King can, in theory, do no wrong, which means he can just whack off your head if he feels like it, or burn your house down, or whatever. (Royal officials do not share this immunity, as the Senate can impeach them for going about doing whatever they please.) In practice, the King rarely goes about breaking the laws because it would quickly lead to a rebellion and his head on a pike. Those unprotected by a House or a Free City had best tread lightly around him, though.
The King can veto any law proposed by the Senate or Great Council, and sets the agenda for Great Council meetings. He can call the Great Council to meet as often as he likes or as not often as he likes, and the same for the Senate.
The King has the right, in person, to go anywhere at all. If he wants to poke around your secret evil laboratory, if he's willing to come in the flesh, he can. He can also demand hospitality for himself and up to five hundred of his closest friends (a trick often used to put financial pressure on people).
The King leads the armies of Chaos in war, and conducts foreign relations and diplomacy.
Chaos has three major forms of law. Royal Edicts are the law of the King's Desmene, and only apply there. House Law are laws promulgated by the individual houses, and only apply in those houses. Finally, Royal Law, which has to be approved by the Senate and Great Council, applies to everyone, everywhere, all the time.
Royal Law and Royal Edicts are enforced by the King's Wardens (aka, the Royal Guardsmen) and crimes under it are tried in the Royal Courts. Every royal shadow has one or more permanent judges, while cases are tried under royal law four times a year in each of the Great Houses, lesser houses, and the free cities by a group of travelling 'circuit' judges. Civil cases are tried by a judge or sometimes a panel of judges, depending on the scale of the case; criminal cases use a judge and jury system.
Cases tried by lesser judges can be appealed to the High Court, where a panel of three judges hears appeals. The High Court also tries cases of criminal action by royal servants, it acts as an advisory board on legal matters to the crown, and it issues writs.
Writs are generally instructions to royal officials to carry out various kinds of actions to resolve matters which have been decided by the courts, or to carry out actions which relate to court cases. A writ might be sent out to the seneschal of a royal estate to conduct a land survey to help determine the truth of a boundary dispute. It might call for prisoners to be released on bail until they are tried. There are many kinds of writs, and improperly filled out writs are not valid.
Some kinds of writs can be levied against House and Free City officials to force them into action, others cannot. It is regrettably easy to escape the King's Justice, if one has the protection of a Great House or Free City. Of course, accepting such protection means it's very hard to ever leave that allegiance...