  It has already been shown, using a local model, that accretion discs with
cooling times t_cool <= 3 Omega^-1 fragment into gravitationally bound objects,
while those with cooling times t_cool > 3 Omega^-1 evolve into a quasi-steady
state. We present results of three-dimensional simulations that test if the
local result still holds globally. We find that the fragmentation boundary is
close to that determined using the local model, but that fragmentation may
occur for longer cooling times when the disc is more massive or when the mass
is distributed in such a way as to make a particular region of the disc more
susceptible to the growth of the gravitational instability. These results have
significant implications for the formation of of gaseous planets in
protoplanetary discs and also for the redistribution of angular momentum which
could be driven by the presence of relatively massive, bound objects within the
disc.
