  We study the Coulomb-to-dipole transition which occurs when the separation
$d$ of an electron-hole bilayer system is varied with respect to the
characteristic in-layer distances. An analysis of the classical ground state
configurations for harmonically confined clusters with $N\leq30$ reveals that
the energetically most favorable state can differ from that of two-dimensional
pure dipole or Coulomb systems. Performing a normal mode analysis for the N=19
cluster it is found that the lowest mode frequencies exhibit drastic changes
when $d$ is varied. Furthermore, we present quantum-mechanical ground states
for N=6, 10 and 12 spin-polarized electrons and holes. We compute the
single-particle energies and orbitals in self-consistent Hartree-Fock
approximation over a broad range of layer separations and coupling strengths
between the limits of the ideal Fermi gas and the Wigner crystal.
