conditions allow outflow, but not inflow. We adopt an $\alpha$ prescription for the viscosity (Shakura and Sunyaev, 1973), with $\alpha=6\times 10^{-3}$, and assume a constant aspect ratio $H/r=4$% in the disk’s equation of state.

Both Jupiter and Saturn initially migrate inward, as expected. The migration of Saturn accelerates exponentially, in a runaway –also called [*Type III*]{}– regime (Masset and Papaloizou, 2003) [that is well fitted by an exponential curve up to $t\sim 100$]{}. After a time of about 100 Jovian initial orbital periods, Saturn crosses the 1:2 mean motion resonance (MMR) with Jupiter, because its migration is [faster than the threshold below which the capture into resonance is certain in the ‘adiabatic’ approximation (Malhotra, 1993): $|\dot{a}_S|/(a_S\Omega_S) << 0.5 j (j+1) \mu_J e_S$, for the $j :
j+1$ resonance, where $\mu_J$ is the mass ratio of Jupiter to the central object, and $a_S$, $e_S$ and $\Omega_S$ are Saturn’s semi-major axis, eccentricity and angular velocity, respectively (MS01).]{}

Once within the 1:2 resonance, Saturn’s runaway migration breaks. This happens because Saturn approaches the outer edge of Jupiter’s gap; thus the disk inside its orbit starts to be partially depleted and consequently Saturn’s coorbital mass deficit becomes smaller that the planet’s own mass (Masset 