  We perform hydrodynamical simulations of the accretion of pebbles and rocks
onto protoplanets of a few hundred kilometres in radius, including two-way drag
force coupling between particles and the protoplanetary disc gas. Particle
streams interacting with the gas far out within the Hill sphere of the
protoplanet spiral into a prograde circumplanetary disc. Material is accreted
onto the protoplanet due to stirring by the turbulent surroundings. We
speculate that the trend for prograde rotation among the largest asteroids is
primordial and that protoplanets accreted 10%-50% of their mass from pebbles
and rocks during the gaseous solar nebula phase. Our model also offers a
possible explanation for the narrow range of spin periods observed among the
largest bodies in the asteroid and trans-Neptunian belts, and predicts that
1000 km-scale Kuiper belt objects that have not experienced giant impacts
should preferentially spin in the prograde direction.
