The impact of non-ideal magnetohydrodynamic processes on discs,
  outflows, counter-rotation and magnetic walls during the early stages of star
  formation
  Non-ideal magnetohydrodynamic (MHD) processes -- namely Ohmic resistivity,
ambipolar diffusion and the Hall effect -- modify the early stages of the star
formation process and the surrounding environment. Collectively, they have been
shown to promote disc formation and promote or hinder outflows. But which
non-ideal process has the greatest impact? Using three-dimensional smoothed
particle radiation non-ideal MHD simulations, we model the gravitational
collapse of a rotating, magnetised cloud through the first hydrostatic core
phase to shortly after the formation of the stellar core. We investigate the
impact of each process individually and collectively. Including any non-ideal
process decreases the maximum magnetic field strength by at least an order of
magnitude during the first core phase compared to using ideal MHD, and promotes
the formation of a magnetic wall. When the magnetic field and rotation vectors
are anti-aligned and the Hall effect is included, rotationally supported discs
of $r \gtrsim 20$~au form; when only the Hall effect is included and the
vectors are aligned, a counter-rotating pseudo-disc forms that is not
rotationally supported. Rotationally supported discs of $r \lesssim 4$~au form
if only Ohmic resistivity or ambipolar diffusion are included. The Hall effect
suppresses first core outflows when the vectors are anti-aligned and suppresses
stellar core outflows independent of alignment. Ohmic resistivity and ambipolar
diffusion each promote first core outflows and delay the launching of stellar
core outflows. Although each non-ideal process influences star formation, these
results suggest that the Hall effect has the greatest influence.
