to open a clean gap (see Fig. \[profiles\]). Thus, [the conditions for a proper Type II migration are never fulfilled (see Crida and Morbidelli, 2007, for a discussion on Type II migration)]{}. If Saturn’s radial migration is not the same as the natural radial motion of the gas, new material flows into its gap. However, the gaps of Jupiter and Saturn overlap, so that material flowing from the outer disk into the coorbital region of Saturn, after experiencing half of a horse-shoe trajectory relative to Saturn, can also perform half of a horse-shoe trajectory relative to Jupiter. The net result is a flow of matter from the outer part of the disk, through the Jupiter-Saturn common gap, into the inner part of the disk. To illustrate this process, Fig. \[profiles\_t\] shows the surface density profile of the disk in the simulation with $H/r=3$%, at various times. Notice how, in first approximation, the Jupiter-Saturn gap simply ‘shifts’ through the disk. As the planets move outward, the disk is rebuilt inside the orbit of Jupiter and the surface density at the bottom of the gap increases as well. Both features are diagnostic of a mass flow through the planets system. In fact, 