When a pawn promotes, does the new piece go to the promotion square, or the home square of piece type it promoted to? In other words, if a pawn promotes to a queen, does the queen go back to the square where the queen starts?
The promoted piece replaces the pawn on the square that the pawn moved to (the 8th rank for White, the 1st rank for Black).
From the FIDE Laws of Chess, (emphasis mine):
3.7.e. When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival.