  A statistical model for the equation of state (EOS) and the composition of
supernova matter is presented with focus on the liquid-gas phase transition of
nuclear matter. It consists of an ensemble of nuclei and interacting nucleons
in nuclear statistical equilibrium. A relativistic mean field model is applied
for the nucleons. The masses of the nuclei are taken from nuclear structure
calculations which are based on the same nuclear Lagrangian. For known nuclei
experimental data is used directly. Excluded volume effects are implemented in
a thermodynamic consistent way so that the transition to uniform nuclear matter
at large densities can be described. Thus the model can be applied at all
densities relevant for supernova simulations, i.e. rho=10^5 - 10^15 g/cm^3, and
it is possible to calculate a complete supernova EOS table. The model allows to
investigate the role of shell effects, which lead to narrow-peaked
distributions around the neutron magic numbers for low temperatures. At larger
temperatures the distributions become broad. The significance of the
statistical treatment and the nuclear distributions for the composition is
shown. We find that the contribution of light clusters is very important and is
only poorly represented by alpha-particles alone. The results for the EOS are
systematically compared to two commonly used models for supernova matter which
are based on the single nucleus approximation. Apart from the composition, in
general only small differences of the different EOSs are found. The differences
are most pronounced around the (low-density) liquid-gas phase transition line
where the distribution of light and intermediate clusters has an important
effect. Possible extensions and improvements of the model are discussed.
