Foreign FCFS and COBE offers are automatically visible for LC users and they can assign a student. The process is explained in more detail in the Local Committees part.
When an AC offer is shared with you, you simply accept the offer.
After that, a button Assign to LCs is available.
Depending on your internal processes, you can decide if you assign the offer to all or only to one LC. You are basically limiting the visibility of this offer to the LC and only the assigned LC(s) can assign a student.
After you assign an LC, you can always change it.
Simply when you are creating a domestic offer, you choose from a list of your LC. The chosen LC can then see the incoming nominations and accept/reject students. It does not get to the sending country without your approval.
If you don't want the LCs to have the possibility to do the above mentioned actions, you don't need to assign the offer to them.