In the rules, it says strongholds are attacked just like cities.   I does not say that they are captured like cities.  In the rules it says that the battle ends immediatly if the stronghold's strength is reduced to zero, but does not say anything about victory points. 

If I assume that strongholds are taken like cities, I would assume that when all nobles retreat, you have the option of rasing cities, so it would make sense that you could raise a stronghold with a partial victory.

So do you have to reduce a stronghold to zero to destroy it, or can you also win with a total or partial victory?

eatjason said:

Page 17 of the rules states that  "The defeated stronghold is then removed from the board". I interprete that as however you defeat the stronghold, wether by reducing it to zero strength,  partial victory /full victory or siege it will be razed (i.e destroyed) and they cannot be captured, as the reward for eliminating a Baron's stronghold is stated as being half  the defeated Baron's gold and one city of the deafeated Baron's choice.   

Wait can you even use victory when taking a stronghold?  I mean how can a Nobel claim a victory over a Barron? Shouldn't you have to take a Stronghold using casualties only?

On the previously-mentioned page 17 of the rules, in the Attacking a Stronghold section, it states: "Strongholds are attacked in exactly the same manner as cities; they may be assaulted or sieged."  I would take this to mean that the rules for Capturing a City Via Assault on page 17 would apply to strongholds, and those rules state: "The attacker may also capture the city by achieving a full or partial victory as described in the 'Count Victories' step of resolving open-field battles."