  Self-gravitating protostellar discs are unstable to fragmentation if the gas
can cool on a time scale that is short compared to the orbital period. We use a
combination of hydrodynamic simulations and N-body orbit integrations to study
the long term evolution of a fragmenting disc with an initial mass ratio to the
star of M_disc/M_star = 0.1. For a disc which is initially unstable across a
range of radii, a combination of collapse and subsequent accretion yields
substellar objects with a spectrum of masses extending (for a Solar mass star)
up to ~0.01 M_sun. Subsequent gravitational evolution ejects most of the lower
mass objects within a few million years, leaving a small number of very massive
planets or brown dwarfs in eccentric orbits at moderately small radii. Based on
these results, systems such as HD 168443 -- in which the companions are close
to or beyond the deuterium burning limit -- appear to be the best candidates to
have formed via gravitational instability. If massive substellar companions
originate from disc fragmentation, while lower-mass planetary companions
originate from core accretion, the metallicity distribution of stars which host
massive substellar companions at radii of ~1 au should differ from that of
stars with lower mass planetary companions.
