  Ground states of three-dimensional EA Ising spin glasses are calculated for
sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact
approximation. For each realization several independent ground states are
obtained. Then, by applying ballistic search and T=0 Monte-Carlo simulations,
it is ensured that each ground state appears with the same probability.
Consequently, the results represent the true T=0 thermodynamic behavior. The
distribution P(|q|) of overlaps is evaluated. For increasing size the width of
P(|q|) and the fraction of the distribution below q_0=0.5 converge to zero.
This indicates that for the infinite system P(|q|) is a delta function, in
contrast to previous results. Thus, the ground-state behavior is dominated by
few large clusters of similar ground states.
