  Type-II migration of giant planets has a speed proportional to the disc's
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 disc's
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 planet's 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 temperature's perturbations.
