  Numerical simulations of pebble dynamics inside gas clumps formed by
gravitational instability of protoplanetary discs are presented. We find that
dust-mediated Rayleigh-Taylor instabilities transport pebbles inward rapidly
via dense metal-rich "fingers". This speeds up sedimentation of small pebbles
by up to two orders of magnitude and yet does not impede grain growth because
grains of all sizes sediment at the same collective speed as long as Stokes
number is less than unity. In simulations with a fixed pebble size, solid
planetary cores form if pebble size exceeds a few cm. Pebble growth leads to
core formation in some hundreds of years even when pebbles injected into clumps
are of mm or smaller sizes. Properties of the gas clump dictate what kind of
cores can be made. Low central temperature clumps allow formation of solid
cores out of refractory materials, whereas in the highest temperature clumps
pebbles of any composition are vaporised and make fuzzy cores only. These
results confirm that gravitational instability of protoplanetary discs is a
robust mechanism of hatching cores from sub-Earth to Neptune mass, as well as
gas giants with massive cores, solid or fuzzy. This mode of planet formation is
especially promising for environs too young and distant (such as the
ALMA-observed HL Tau disc) or too violent (such as circum-binary planets) to
form via the Core Accretion scenarios.
