Type-II migration of giant planets has a speed proportional to the discs viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations using 2D (including self-gravity) and 3D codes. After selecting disc masses for which self-gravity is not important, 3D simulations without self-gravity can be safely used. In our nominal simulation only numerical viscosity is present. We then performed simulations with prescribed viscosity to assess the threshold below which the new migration processes appear. We show that for alpha viscosity <= 1.e-5 two migration modes are possible which differ from classical Type-II migration, in the sense that they are not proportional to the discs viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. We call this type of migration vortex-driven migration. This migration is very slow and cannot continue indefinitely, because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planets eccentricity grows to a value ~0.2 due to inefficient eccentricity damping by corotation resonances. This second, faster migration mode appears to be typical of 2D models in discs with slower damping of temperatures perturbations.
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