it is usually the agency who has discovered the girl. That means that most eastern, Brasilian...have usually still thei mother agency in their home country even when they become quiet famous.
It is a special contract, as usually the mother agency has the world exclusiv right on the model, so it is them who decide the girl placement in agencies partners all over the world.
The possibility of changing of mother agency depend of each contract, also in case of good offer, the mother agency can decide just to sell the contract to an agency ready to buy it.
In the big agencies, some, like Next or Women like to be mother agency, so they often offer to buy (or sometimes try to steal...) the contract to the orginal mother agencies, some other like IMG are not much interested by that, and usually deal with the girl's original mother agency during all the model carreer...