Question about spoils

Each spoil has a territory name on it. Is this a random territory drawn from the board for each player every turn or are the territories drawn for each player according to what is remaining on the board (if the board can support it)? I know how multiple players can hold the same card on small maps; but is this true even if the board has enough territories?
As an example, if 5 players all had 5 cards on the classic map, will no 2 players hold the same territory on any of their spoils?
As an example, if 5 players all had 5 cards on the classic map, will no 2 players hold the same territory on any of their spoils?