  The possibility to draw links between the isospin properties of nuclei and
the structure of compact stars is a stimulating perspective. In order to pursue
this objective on a sound basis, the correlations from which such links can be
deduced have to be carefully checked against model dependence. Using a variety
of nuclear effective models and a microscopic approach, we study the relation
between the predictions of a given model and those of a Taylor density
development of the corresponding equation of state: this establishes to what
extent a limited set of phenomenological constraints can determine the
core-crust transition properties. From a correlation analysis we show that a)
the transition density $\rho_t$ is mainly correlated with the symmetry energy
slope $L$, b) the proton fraction $Y_{p,t}$ with the symmetry energy and
symmetry energy slope $(J,L)$ defined at saturation density, or, even better,
with the same quantities defined at $\rho=0.1$ fm$^{-3}$, and c) the transition
pressure $P_t$ with the symmetry energy slope and curvature $(J,K_{\rm sym})$
defined at $\rho=0.1$ fm$^{-3}$.
