I usually don't have family ties spread against continental boundaries. However, if a character of your family makes an enemy of me large enough on one continent, all members of that family will be my enemy on that continent.
THe other continents will be different, because the way that I RP my characters is that they are brothers which never got along. So they don't talk much, and often I've had a character get back at his older brother by working with a family that one of them hated.
Not to say a few characters and families haven't reached the "bad" list, and some haven't reached the good list.
