In the original Star Wars movie, Luke lives with Uncle Owen and Aunt Beru, who talk about how Luke is like his father. When Luke discovers that Vader is his father in ESB, and then tells Leia, it is implied that Leia was raised by their mother who Luke never knew.
Obviously, this is not how the prequels portray this; they instead have Padme die in childbirth and Luke is sent to live with Owen and Beru. Anakin's mother married Owen's father, technically making Owen Anakin's stepbrother and Luke's uncle. But this is a pretty far removed method of relating them - and it certainly doesn't seem like the original plan.
What was the original relationship between Luke and his aunt and uncle? Was Uncle Owen supposed to be his father's brother? As Leia is a princess, it would seem to make sense that she was raised by their mother, who was a queen, and likely doesn't have a sibling living on Tatooine.