We have performed smoothed particle radiation magnetohydrodynamics ( SPRMHD ) simulations of the collapse of rotating , magnetised molecular cloud cores to form protostars . The calculations follow the formation and evolution of the first hydrostatic core , the collapse to form a stellar core , the launching of outflows from both the first hydrostatic core and stellar cores , and the breakout of the stellar outflow from the remnant of the first core . We investigate the roles of magnetic fields and thermal feedback on the outflow launching process , finding that both magnetic and thermal forces contribute to the launching of the stellar outflow . We also follow the stellar cores until they grow to masses of up to 20 Jupiter-masses , and determine their properties . We find that at this early stage , before fusion begins , the stellar cores have radii of \approx 3 R _ { \odot } with radial entropy profiles that increase outward ( i.e . are convectively stable ) and minimum entropies per baryon of s / k _ { B } \approx 14 in their interiors . The structure of the stellar cores is found to be insensitive to variations in the initial magnetic field strength . With reasonably strong initial magnetic fields , accretion on to the stellar cores occurs through inspiralling magnetised pseudo-discs with negligible radiative losses , as opposed to first cores which effectively radiate away the energy liberated in the accretion shocks at their surfaces . We find that magnetic field strengths of > 10 kG can be implanted in stellar cores at birth .