  We investigate the evolution of protoplanets with different masses embedded
in an accretion disk, via global fully three-dimensional hydrodynamical
simulations. We consider a range of planetary masses extending from one and a
half Earth's masses up to one Jupiter's mass, and we take into account
physically realistic gravitational potentials of forming planets. In order to
calculate accurately the gravitational torques exerted by disk material and to
investigate the accretion process onto the planet, the flow dynamics has to be
thoroughly resolved on long as well as short length scales. We achieve this
strict resolution requirement by applying a nested-grid refinement technique
which allows to greatly enhance the local resolution. Our results from
altogether 51 simulations show that for large planetary masses, approximately
above a tenth of the Jupiter's mass, migration rates are relatively constant,
as expected in type II migration regime and in good agreement with previous
two-dimensional calculations. In a range between seven and fifteen Earth's
masses, we find a dependency of the migration speed on the planetary mass that
yields time scales considerably longer than those predicted by linear
analytical theories. This property may be important in determining the overall
orbital evolution of protoplanets. The growth time scale is minimum around
twenty Earth-masses, but it rapidly increases for both smaller and larger mass
values. Significant differences between two- and three-dimensional calculations
are found in particular for objects with masses smaller than ten Earth-masses.
We also derive an analytical approximation for the numerically computed mass
growth rates.
