Those who give away characters are indeed giving the recipient the character both reference-wise, preset-wise and altogether. Once someone has 'adopted' the oc they're giving away, the oc then completely belongs to the one who bought it and no longer by it's previous owner. The new owner can then make the size up for themselves if given permission, although often it's just a "take it and change it however you like" when it comes to selling/adopting OCs.
