  We investigate the formation of binary stellar systems. We consider a model
where a `seed' protobinary system forms, via fragmentation, within a collapsing
molecular cloud core and evolves to its final mass by accreting material from
an infalling gaseous envelope. This accretion alters the mass ratio and orbit
of the binary, and is largely responsible for forming the circumstellar and/or
circumbinary discs. Given this model for binary formation, we predict the
properties of binary systems and how they depend on the initial conditions
within the molecular cloud core. We predict that there should be a continuous
trend such that closer binaries are more likely to have equal mass components
and are more likely to have circumbinary discs than wider systems. Comparing
our results to observations, we find that the observed mass-ratio distributions
of binaries and the frequency of circumbinary discs as a function of separation
are most easily reproduced if the progenitor molecular cloud cores have radial
density profiles between uniform and 1/r (e.g. Gaussian) with near
uniform-rotation. This is in good agreement with the observed properties of
pre-stellar cores. Conversely, we find that the observed properties of binaries
cannot be reproduced if the cloud cores are in solid-body rotation and have
initial density profiles which are strongly centrally condensed. Finally, in
agreement with the radial-velocity searches for extra-solar planets, we find
that it is very difficult to form a brown dwarf companion to a solar-type star
with a separation < 10 AU, but that the frequency of brown dwarf companions
should increase with larger separations or lower mass primaries.
