To th victor go the spoils

[Peasant Phill]

I just had my first joined siege. I, as the Date, attacked the last Ikko stronghold with a full Hattori stack in the province. The Hattori joined the siege assault. In the end I conquered the province but this got me wondering how this was established.
In the old MTW, the army with the most men left got the province. Is this still the case?

[Poulp']

As far as I saw, the province goes to the sieging army.

On two occasions, I joined a siege as reinforcement and the provinces went to the AI (Hattori while playing Oda, (Shoni/Ouchi?) as Shimazu.)
Mind you, with those armies, I never reached the central keep.

[Vladimir]

I believe in Medieval 2 it was whoever launched the attack. I'd set siege with a minimum of forces and let my allies take the city. My general would march in triumphant just as the city was about to fall.