  We present results from radiation non-ideal magnetohydrodynamics (MHD)
calculations that follow the collapse of rotating, magnetised, molecular cloud
cores to stellar densities. These are the first such calculations to include
all three non-ideal effects: ambipolar diffusion, Ohmic resistivity and the
Hall effect. We employ an ionisation model in which cosmic ray ionisation
dominates at low temperatures and thermal ionisation takes over at high
temperatures. We explore the effects of varying the cosmic ray ionisation rate
from $\zeta_\text{cr}= 10^{-10}$ to $10^{-16}$ s$^{-1}$. Models with ionisation
rates $\gtrsim 10^{-12}$ s$^{-1}$ produce results that are indistinguishable
from ideal MHD. Decreasing the cosmic ray ionisation rate extends the lifetime
of the first hydrostatic core up to a factor of two, but the lifetimes are
still substantially shorter than those obtained without magnetic fields.
Outflows from the first hydrostatic core phase are launched in all models, but
the outflows become broader and slower as the ionisation rate is reduced. The
outflow morphology following stellar core formation is complex and strongly
dependent on the cosmic ray ionisation rate. Calculations with high ionisation
rates quickly produce a fast (~14km s$^{-1}$) bipolar outflow that is distinct
from the first core outflow, but with the lowest ionisation rate a slower (~3-4
km s$^{-1}$) conical outflow develops gradually and seamlessly merges into the
first core outflow.
