  We investigate the formation and fragmentation of discs using a suite of
three-dimensional smoothed particle radiative magnetohydrodynamics simulations.
Our models are initialised as 1M$_\odot$ rotating Bonnor-Ebert spheres that are
threaded with a uniform magnetic field. We examine the effect of including
ideal and non-ideal magnetic fields, the orientation and strength of the
magnetic field, and the initial rotational rate. We follow the gravitational
collapse and early evolution of each system until the final classification of
the protostellar disc can be determined. Of our 105 models, 41 fragment, 21
form a spiral structure but do not fragment, and another 12 form smooth discs.
Fragmentation is more likely to occur for faster initial rotation rates and
weaker magnetic fields. For stronger magnetic field strengths, the inclusion of
non-ideal MHD promotes disc formation, and several of these models fragment,
whereas their ideal MHD counterparts do not. For the models that fragment,
there is no correlation between our parameters and where or when the
fragmentation occurs. Bipolar outflows are launched in only 17 models, and
these models have strong magnetic fields that are initially parallel to the
rotation axis. Counter-rotating envelopes form in four slowly-rotating,
strong-field models -- including one ideal MHD model -- indicating they form
only in a small fraction of the parameter space investigated.
