  We present analytic models for the local structure of self-regulated
self-gravit ating accretion discs that are subject to realistic cooling. Such
an approach can be used to predict the secular evolution of self-gravitating
discs (which can usefully be compared with future radiation hydrodynamical
simulations) and to define various physical regimes as a function of radius and
equivalent steady state accretion rate. We show that fragmentation is
inevitable, given realistic rates of infall into the disc, once the disc
extends to radii $> 70$ A.U. (in the case of a solar mass central object).
Owing to the outward redistribution of disc material by gravitational torques,
we also predict fragmentation at $> 70$ A.U. even in the case of low angular
momentum cores which initially collapse to a much smaller radius. We point out
that 70 A.U. is close to the median binary separation and propose that such
delayed fragmentation, at the point that the disc expands to $> 70$ A.U.,
ensures the creation of low mass ratio companions that can avoid substantial
further growth and consequent evolution towards unit mass ratio. We thus
propose this as a promising mechanism for producing low mass ratio binaries,
which, while abundant observationally, are severely underproduced in
hydrodynamical models.
