Giant planet embryos are believed to be spawned by gravitational instability
in massive extended (R ~ 100 AU) protostellar discs. In a recent paper we have
shown that dust can sediment inside the embryos, as argued earlier by Boss
(1998) in a slightly different model. Here we study numerically the next stage
of this process -- the formation of a solid core. If conditions are conducive
to solid core formation, the centre of the gas cloud goes through the following
sequence of phases: (i) becomes grain (and metal) rich; (ii) forms a
terrestrial mass solid core via a rapid collapse driven by self-gravity of the
grains; (iii) starts to accrete a gaseous atmosphere when the solid core
reaches mass of a few to 10 Earth masses. This sequence of events may build
either terrestrial planet cores or metal rich giant planets inside the larger
gas reservoir of the giant planet embryo. In a companion Letter we argue that
tidal and irradiation effects from the parent star should disrupt the outer
metal poor layers of the embryo, releasing nearly "ready to use" planets. We
propose this as an alternative way to build planets.Comment: 20 pages, submitted to MNRAS, referred to as "paper II" in serie
