  We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick
systems of L^3 spins. After averaging over large sets of EA system samples of 3
=< L =< 10, we obtain accurate numbers for distributions p(q) of the overlap
parameter q at very low temperature T. We find p(0)/T --> 0.233(4) as T --> 0.
This is in contrast with the droplet scenario of spin glasses. We also study
the number of mismatched links --between replica pairs-- that come with large
scale excitations. Contributions from small scale excitations are discarded. We
thus obtain for the fractal dimension of outer surfaces of q~0 excitations in
the EA model d_s --> 2.59(3) as T tends to 0. This is in contrast with d_s -->
3 as T --> 0 that is predicted by mean field theory for the macroscopic limit.
