smoothing length. In Sect. \[accrete\] we briefly address the effect of the accretion of mass onto the planets, already partially discussed in MS01. In Sect. \[masses\] we explore the dynamics for different values of the planet masses, to understand how generic the MS01 mechanism can be for extra-solar planet cases. In Sect. \[resonance\] we discuss possible ways to reconcile the MS01 mechanism with the LHB model of Gomes et al. Our conclusions are then recollected in the summary section.

The Masset–Snellgrove mechanism {#MS}
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Fig. \[MS-orig\] is a quite close reproduction of Fig. 1 in MS01. It has been obtained using the code presented in Masset (2000a,b) (the same as used in MS01), with similar parameters. Specifically, Jupiter is initially at $r=1$, while Saturn is at $r=2$. The disk extends from $r=0.3$ to 5. It is modeled in two dimensions, using a grid with resolution 282 in radius and 325 in azimuth. Its initial surface density is uniform in radius and is equal to $6\times 10^{-4}$ in our units (the mass of the Sun is 1), which corresponds to the surface density of the minimal mass nebula (Hayashi, 1981) if the unit of length corresponds to 5 AU. The boundary 