I don't know about potatoes, but here's the story on ham:
Moe's wife sent him to the store for a ham. After he got home,
she asked him why he didn't have the butcher cut off the end
of the ham. Moe asked his wife why she wanted the end cut off.
She replied that her mother had always done it that way and
that was reason enough for her. Since the wife's mother was
visiting, they asked her why she always cut off the end of
the ham. Mother replied that this was the way /her/ mother
did it; Mother, daughter, and Moe then decided to call grandmother
and solve this three-generation mystery. Grandmother promptly
replied that she cut the end of the ham because her roaster
was too small to cook it in one piece.
Combining two recent threads: How does the cooking time
scale with the mass of the potato?
Also: There is such a thing as a half-baked potato. I
think of it more as a baked half-potato: Cut the spud
in half the long way, and then place it flat-side down
on a baking sheet in the oven.