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 $(L,K_{\rm sym})$ defined at $\rho=0.1$ fm$^{-3}$.