  We use time-dependent, one-dimensional disc models to investigate the
evolution of protostellar discs that form through the collapse of molecular
cloud cores and in which the primary transport mechanism is self-gravity. We
assume that these discs settle into a state of thermal equilibrium with Q = 2
and that the strength of the angular momentum transport is set by the cooling
rate of the disc. The results suggest that these discs will attain a
quasi-steady state that persists for a number of free-fall times and in which
most of the mass within 100 au is located inside 10-20 au. This pile-up of mass
in the inner disc could result in temperatures that are high enough for the
growth of MHD turbulence which could rapidly drain the inner disc and lead to
FU Orionis-like outbursts. In all our simulations, the inner regions of the
discs (r < 40 au) were stable against fragmentation, while fragmentation was
possible in the outer regions (r > 40 au) of discs that formed from cores that
had enough initial angular momentum to deposit sufficient mass in these outer
regions. The large amounts of mass in these outer regions, however, suggests
that fragmentation will lead to the formation of sub-stellar and stellar mass
companions, rather than planetary mass objects. Although mass accretion rates
were largely consistent with observations, the large disc masses suggest that
an additional transport mechanism (such as MRI occuring in the upper layers of
the disc) must operate in order to drain the remaining disc material within
observed disc lifetimes.
