[Retros] Current best solutions to my task :

[Nicolas.Dupont at math.univ-lille1.fr]

King without capture : 5.5 moves  (Noam Elkies)
1.d4 f6 2.Qd3 Kf7 3.Qh3 Kg6 4.Kd2 Kg5 5.Nc3 Kf4 6.Ke1#
King with capture : not least

Knight without capture : 6 moves (Itamar Faybish)
1.e3 e6 2.Ke2 Bd6 3.Kf3 Qf6+ 4.Kg4 Ne7 5.Kh5 g6+ 6.Kh6 Ng8#
Knight with capture : not least

Queen without capture : 6 moves  (Joachim Iglesias)
1.d3 d6 2.Kd2 Bd7 3.Kc3 Qc8 4.Kb4 c5+ 5.Ka5 Bc6 6.b4 Qd8#
Queen with capture : not least

Bishop without capture : 6.5 moves (Itamar Faybish)
1.e4 e5 2.Ne2 Ke7 3.Nec3 Kf6 4.Be2 Kg5 5.d3+ Kh4 6.g3+ Kh3 7.Bf1#
Bishop with capture : not least

Rook without capture : 7.5 moves (Noam Elkies)
1.h4 e6 2.h5 Qh4 3.h6 Qe4 4.f4 f6 5.Nf3 Kf7 6.Rg1 Kg6 7. Ne5+ Kh5 8.Rh1#
Rook with capture : 6 moves (Joachim Iglesias)
1.e3 e6 2.Ke2 Ne7 3.Kf3 Rg8 4.Kg4 h5+ 5.Kxh5 Nec6 6.Qg4 Rh8#