In this paper, we modify Laskar's simplified model of planetary evolution and
accretion [J. Laskar, Phys. Rev. Lett, vol 84, p 3240 (2000)] to account for
the full conservation of the total angular momentum of the system, and extend
it to incorporate an accretion probability that depends on the mass and
relative velocity of the colliding particles. We present statistical results
for the mass and eccentricity of the planets formed, in terms of their
semi-major axes, for a large number of realisations of different versions of
the model. In particular, we find that by combining the mass-dependent
accretion probability and the velocity-selection mechanism, the planets formed
display a systematic occurrence at specific locations. By introducing properly
scaled variables, our results are universal with respect to the total angular
momentum of the system, the mass of the planetesimal disc, and the mass of the
central star.Comment: 13 pages, 21 figures, some in colour. Accepted in MNRA
