  We analyse the non-linear, three-dimensional response of a gaseous, viscous
protoplanetary disc to the presence of a planet of mass ranging from one Earth
mass (1 M$_e$) to one Jupiter mass (1 M$_J$) by using the ZEUS hydrodynamics
code. We determine the gas flow pattern, and the accretion and migration rates
of the planet. The planet is assumed to be in a fixed circular orbit about the
central star. It is also assumed to be able to accrete gas without expansion on
the scale of its Roche radius. Only planets with masses $M \gsim 0.1$ M$_J$
produce significant perturbations in the disc's surface density. The flow
within the Roche lobe of the planet is fully three-dimensional. Gas streams
generally enter the Roche lobe close to the disc midplane, but produce much
weaker shocks than the streams in two-dimensional models. The streams supply
material to a circumplanetary disc that rotates in the same sense as the
planet's orbit. Much of the mass supply to the circumplanetary disc comes from
non-coplanar flow. The accretion rate peaks with a planet mass of approximately
0.1 M$_J$ and is highly efficient, occurring at the local viscous rate. The
migration timescales for planets of mass less than 0.1 M$_J$, based on torques
from disc material outside the planets' Roche lobes, are in excellent agreement
with the linear theory of Type I (non-gap) migration for three-dimensional
discs. The transition from Type I to Type II (gap) migration is smooth, with
changes in migration times of about a factor of 2. Starting with a core which
can undergo runaway growth, a planet can gain up to a few M$_J$ with little
migration. Planets with final masses of order 10 M$_J$ would undergo large
migration, which makes formation and survival difficult.
