  Protoplanet eccentricities of e >~ H/r can slow or reverse migration, but
previous 2D studies have shown that gravitational scattering cannot maintain
significant planet eccentricities against disc-induced damping. We simulate the
evolution of low-mass protoplanetary swarms in three dimensions. The aim is to
examine both protoplanet survival rates and the dynamical structure of the
resulting planetary systems, and to compare them with 2D simulations. We
present results from a 3D hydrodynamic simulation of eight protoplanets
embedded in a protoplanetary disc. We also present a suite of simulations
performed using an N-body code, modified to include prescriptions for planetary
migration and for eccentricity and inclination damping. These prescriptions
were obtained by fitting analytic formulae to hydrodynamic simulations of
planets embedded in discs with initially eccentric and/or inclined orbits. As
was found in two dimensions, differential migration produces groups of
protoplanets in stable, multiple mean-motion resonances that migrate in
lockstep, preventing prolonged periods of gravitational scattering. In almost
all simulations, this leads to large-scale migration of the protoplanet swarm
into the central star in the absence of a viable stopping mechanism. The
evolution involves mutual collisions, occasional instances of large-scale
scattering, and the frequent formation of the long-lived, co-orbital planet
systems that arise in > 30% of all runs. Disc-induced damping overwhelms
eccentricity and inclination growth due to planet-planet interactions.
Co-orbital planets are a natural outcome of dynamical relaxation in a strongly
dissipative environment, and if observed in nature would imply that such a
period of evolution commonly arises during planetary formation.
