(sorry for my english, thats not my native language, you can point me on typos though)
In BoA, units of different nationalities can be in the same province at the same time. Even if enemy, they can stay facing each other without fighting. How can it be? This is defined by the posture you give to your armies. For example, taking an historical example, in early 1775, what will become the Continental army was containing the British, in the province of Boston. The British
were not inside the walls whats more, but were deployed outside.
This can be simulated in BoA, by having both armies in defensive posture. The advantage of the defensive posture is that you benefit from terrain, and entranchment.
Now,what about the city, fort, whatever? If you decide to put your army "inside the walls" (well a city is unwalled, but you get the idea, you are in the city) and you have an enemy in the province, then a siege occurs.
If the enemy want to storm the city (or fort), then he has to choose the Assault posture, but if he prefers, he can siege it, and thats the object of your question

Siege are rather well detailed in BoA. I'm not speaking here of fancy animations (although you have indicators on the map that your army is besieging something, or, in the contrary, that you are being besieged (and blockaded/ in open harbor if the city has a port)), but of the mechanics of siege:
The exact mechanic of siege is rather complex, but the possible results of a month of siege are:
1. nothing achieved
2. defenders suffers hits from opposing army bombardment.
3. a breach has been done (can be cumulative with 2)
4. defenders surrenders
on top of that, you have the normal supply/attrition phase, with supply stock being reduced for the defender, etc.
After a given number of breaches, the city/fort does not provide defensive bonus anymore. Its generally the sign that the attacker wil assault

Surrender is computed by taking into consideration troops quality and current supply status.
Now, what about artillery and friendly fleet adjacent to a coastal city: these units provide big bonus for the siege result roll. A fleet near New York city for example would surely inflict hits and perhaps breaches each month to a besieged opponent. Naval superiority has some worth
