somerandomdude, I think the centre of the map would be Rome. All roads do lead there after all.
As for claiming duchies on behalf of other people, they won't automatically become your vassal unless the prospective duke is either a member of your dynasty or would be your de jure vassal. For example if you're playing as the king of Scotland and press your brother's claim on the duchy of Northumberland then he'll become your vassal (and part of Scotland) should you win, whereas if you claim the duchy for a random Saxon exile in your court then Northumberland will become independent because he's neither a member of your dynasty nor a de jure vassal of Scotland.
As for claiming duchies on behalf of other people, they won't automatically become your vassal unless the prospective duke is either a member of your dynasty or would be your de jure vassal. For example if you're playing as the king of Scotland and press your brother's claim on the duchy of Northumberland then he'll become your vassal (and part of Scotland) should you win, whereas if you claim the duchy for a random Saxon exile in your court then Northumberland will become independent because he's neither a member of your dynasty nor a de jure vassal of Scotland.