What rearrangent of the starting position's pieces, in any manner, has the fastest stalemate? It is well known that the fastest stalemate is in 19 ply. But what is the fastest possible if all pieces, not pawns, may be shuffled at will on their first ranks? This will be difficult since there is much to consider, but 19 ply is certainly beatable.
I don't know if this is the fastest, but I managed to shave one ply off of the standard chess example by moving the queen to a better starting square. This allows the side giving stalemate to start capturing one move sooner, resulting in stalemate in 18 ply instead of 19.

[Result "1/2-1/2"]
[FEN "rnbnqbkr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQ - 0 1"]

1. a4 d6 2. Ra3 Qxa4 3. h4 h5 4. Rah3 Qxc2 5. f3 Qxd2+ 6. Kf2 Qxb2 7. Qxd6 Qxb1 8. Qh2 Qxc1 9. Kg3 Qe3 1/2-1/2