Parameters for the planetary growth timescale (Eq. (A.1)) obtained from the comparison of numerical simulations (Sect. 3) with the semi-analytical solution of Sect. A.1. The upper panel shows the exponent p as a function of f_opa. The initial surface density of planetesimals is 10 (top, black), 6 (middle, red) and 4 g/cm² (bottom, blue line). The lower panel shows b, again as function of f_opa and the three planetesimal surface densities. Thick lines are the numerical results, while thin lines give the approximative linear scaling with f_opa.