  The effects of $\delta$ mesons on the dynamical instabilities of cold and
warm nuclear and stellar matter at subsaturation densities are studied in the
framework of relativistic mean-field hadron models (NL3, NL$\rho$ and
NL$\rho\delta$) with the inclusion of the electromagnetic field. The
distillation effect and the spinodals for all the models considered are
discussed. The crust-core transition density and pressure are obtained as a
function of temperature for $\beta$-equilibrium matter with and without
neutrino trapping. An estimation of the size of the clusters formed in the
non-homogeneous phase is made. It is shown that cluster sizes increase with
temperature. The effects of the $\delta$-meson on the instability region are
larger for low temperatures, very asymmetric matter and densities close to the
spinodal surface. It increases the distillation effect above $\sim 0.4\rho_0$
and has the opposite effect below that density.
