The properties spread around the map are collectively referred to as fiefs. A fief can be a castle, town, or village. Each is owned by someone, and they can change hands over time. There are various ways to acquire fiefs for yourself.
If you besiege a town or castle when not in a faction it will automatically become your property at the end of the siege. Holding a fief on your own is difficult because the other factions can declare war on you at any time and will arrive in force to take your lands from you. For more information, see the factions page.
Reward for allegiance
Once you have at least 150 Renown, kings will start randomly asking you to pledge your allegiance, offering you a village to sweeten the deal. If you refuse an offer you will lower your relations with the leader offering it, making him less likely to make a future offer; once his opinion of you is a negative value he will stop asking you. Factions you have negative relations with will not offer allegiance.
If you ask the king yourself, certain calculations are involved to determine whether you are worthy of becoming a vassal (refer to joining a faction for more information).
Regardless of the method in which you joined the faction, the king will grant you the poorest village his faction currently possesses. If the village belongs to a castle (e.g. Slezh), then the lord who owns the castle will become your enemy with a relation of -25, and you will not be allowed to enter the castle. However, if you meet the lord, you can do his quests to ameliorate your relations with him, for example if there is something in the castle that he owns which is of use to you.
Reward for sieges
Armies frequently besiege towns and castles in addition to fighting each other directly; once you have joined a faction you can besiege locations yourself (see siege for details). When a location is captured it becomes the property of the victorious faction; if there is a village nearby that will also become that faction's property.
Every time a castle or town is conquered the king will give it to one of his vassals, and the village(s) to a different vassal; if you are a member of that faction there is a chance that you will receive one of these new assets, especially if you were the one who besieged it. If you captured it yourself you can specifically ask for that town or castle from the location menu to increase your chance of getting it, but there is also a chance that the king will give it to you without you asking.
If you are offered a fief you have the choice of accepting or refusing; if you refuse it will go to another vassal instead. The calculations used to determine which vassal gets a property are partly based on renown, your relationship with the king, and luck, so there is no easy way of determining whether you'll be offered a fief after you capture a town or castle.
When you are granted a town or castle your banner will fly above it on the world map, clearly identifying it as your property (villages do not display a banner). You also get the right to collect taxes from it.
Regardless of how you acquire a fief, doing so allows you to collect taxes from the populace on a weekly basis (these taxes accumulate, so you don't have to visit every week if you don't want to). Generally speaking, towns will earn the most taxes, villages second, and castles last. The individual prosperity of each location also plays a role.
Contrary to what many sources say, you CANNOT raise the prosperity of a town by ensuring its caravans reach their destinations, nor can you affect it by getting quests from the Guildmaster. The ONLY time a town increases in prosperity is if a caravan from ANOTHER town visits it. When a visiting caravan enters a town, the game makes the first of two checks, and randomly decides if the town's prosperity increases or not. If the first check succeeds, the prosperity of the town increases slightly. If the first check fails, prosperity remains the same, a second check is then made, the success rate of which is dependent on the town's current prosperity. If the town the caravan visits is already wealthy, the chances for the second check to succeed are lower. However, if the town is poorer, the chances that the second check succeeds are higher. In any event, a town can only succeed at either the first or second check; in other words, per caravan visit, a town can only gain prosperity once. The only way to help a town gain prosperity therefore is to ensure that caravans en route to it make it safely. A town also has a relatively high probability of losing prosperity while under siege.
For villages, the process by which prosperity is increased is similar. In their case, however, prosperity has a slight chance of increasing if their villagers make it to town and back successfully. Every villager that makes it back to the village has a small chance of increasing prosperity. A village will always lose prosperity if it is looted, and it will also when it is infested by bandits. If raided, prosperity decreases once the village has been successfully looted. If infested, it will gradually lose prosperity per 3 days of bandit infestation. Ensure it is not raided, kill bandits if they invade it, and build improvements. Again, contrary to what some sources claim, getting quests from the Village Elder DOES NOT improve prosperity EXCEPT for two specific quests: "Deliver Cattle" and "Deliver Grain". For more details, see the individual pages on towns and villages.
Once a village belongs to you or to your faction you can no longer loot it, although you can still force the peasants to give you supplies. If you have previously burned a village that becomes your fief the townsfolk will remember and hate you, but you can still collect your taxes as usual. You will however be unable to get Recruits from this village (see Recruiting). You can see your reputation in the description at the top along with a word describing how much they like or hate you ("acceptive", "resentful", "hate you with a passion", etc.)
As a general rule, if you intend to take part in sieges to earn further fiefs for yourself you may want to avoid raiding nearby villages belonging to that same faction so that they will still like you. Burning villages decreases their prosperity (which affects the taxes and recruits you can collect), so it is in your best interest to ensure any villages you may come to inherit are in as good a condition as possible.