  We develop a phenomenological statistical model for dilute star matter at
finite temperature, in which free nucleons are treated within a mean-field
approximation and nuclei are considered to form a loosely interacting cluster
gas. Its domain of applicability, that is baryonic densities ranging from about
$\rho>10^8$ g $\cdot$ cm$^{-3}$ to normal nuclear density, temperatures between
1 and 20 MeV and proton fractions between 0.5 and 0, make it suitable for the
description of baryonic matter produced in supernovae explosions and
proto-neutron stars. The first finding is that, contrary to the common belief,
the crust-core transition is not first order, and for all subsaturation
densities matter can be viewed as a continuous fluid mixture between free
nucleons and massive nuclei. As a consequence, the equations of state and the
associated observables do not present any discontinuity over the whole
thermodynamic range. We further investigate the nuclear matter composition over
a wide range of densities and temperatures. At high density and temperature our
model accounts for a much larger mass fraction bound in medium nuclei with
respect to traditional approaches as Lattimer-Swesty, with sizeable
consequences on the thermodynamic quantities. The equations of state agree well
with the presently used EOS only at low temperatures and in the homogeneous
matter phase, while important differences are present in the crust-core
transition region. The correlation among the composition of baryonic matter and
neutrino opacity is finally discussed, and we show that the two problems can be
effectively decoupled.
