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The critical properties for the transition to warm, asymmetric, non-homogeneous nuclear matter are analysed within a thermodynamical spinodal approach for a set of well calibrated equations of state. It is shown that even though different equations of state are constrained by the same experimental, theoretical and observational data, and the properties of symmetric nuclear matter are similar within the models, the properties of very asymmetric nuclear matter, such as the one found inside of neutron stars, differ a lot for various models. Some models predict larger transition densities to homogeneous matter for beta-equilibrated matter than for symmetric nuclear matter. Since one expects that such properties have a noticeable impact on the the evolution of either a supernova or neutron star merger, this different behavior should be understood in more detail., 13 pages, 10 figures, 4 tables; accepted for publication in PRC

The influence of the uncertainties of the equation of state empirical parameters on the neutron stars crust-core phase transition is explored within a meta-modeling approach, in which the energy per particle is expanded as a Taylor series in density and asymmetry around the saturation point. The phase transition point is estimated from the intersection of the spinodal instability region for dynamical fluctuations with the chemical equilibrium curve. Special attention is paid to the inclusion of high-order parameters of the Taylor series and their influence on the transition point. An uncorrelated prior distribution is considered for the empirical parameters, with bulk properties constrained through effective field theory predictions, while the surface parameters are controlled from a fit of nuclear masses using the extended Thomas Fermi approximation. The results show that the isovector compressibility $K_{sym}$ and skewness $Q_{sym}$ have the most significant correlations with the transition point, along with the previously observed influence of the $L_{sym}$ parameter. The estimated density and pressure of the crust-core transition are $n_t = (0.071 \pm 0.011) fm^{-3}$ and $P_t = (0.294 \pm 0.102) MeV fm^{-3}$., 11 pages, 7 figures