  We report results from radiation hydrodynamical simulations of the collapse
of molecular cloud cores to form protostars. The calculations follow the
formation and evolution of the first hydrostatic core/disc, the collapse to
form a stellar core, and effect of stellar core formation on the surrounding
disc and envelope. Past barotropic calculations have shown that
rapidly-rotating first cores evolve into `pre-stellar discs' with radii up to
~100 AU that may last thousands of years before a stellar core forms. We
investigate how the inclusion of a realistic equation of state and radiative
transfer alters this behaviour, finding that the qualitative behaviour is
similar, but that the pre-stellar discs may last 1.5-3 times longer in the more
realistic calculations. The masses, radii, and lifetimes of the discs increase
for initial molecular cloud cores with faster rotation rates. In the most
extreme case we model, a pre-stellar disc with a mass of 0.22 Msun and a radius
of ~100 AU can form in a solar-mass cloud and last several thousand years
before a stellar core is formed. Such large, massive objects may be imaged
using ALMA. Fragmentation of these massive discs may also provide an effective
route to binary and multiple star formation, before radiative feedback from
accretion onto the stellar core can inhibit fragmentation. Once collapse to
form a stellar core occurs within the pre-stellar disc, the radiation
hydrodynamical simulations produce qualitatively different behaviour from the
barotropic calculations due to the accretion energy released. This drives a
shock wave through the circumstellar disc and launches a bipolar outflow even
in the absence of magnetic fields.
