I present results from a set of numerical simulations of star formation with a restricted set of physics designed to isolate and understand basic processes.  Cloud simulations of star (sink) formation which develop a large dynamic range in mass beyond fragmentation limits and good number statistics robustly show the development of a power law mass function dN/dlog M ~ M^-1.  We demonstrate that this result naturally arises from a variant of Bondi-Hoyle accretion, which holds despite the complexity of the accreting environment, time-variability, self-gravity, etc.  The power law M^-1 is an asymptotic result when masses grow far beyond initial fragment values; we suggest that the Salpeter slope -1.35 is a result of limited mass growth in some regions, and predict that the flatter -1.0 limit should be more easily attained in dense, massive star-forming regions.  I then turn to very recent simulations of magnetized protostellar cloud core formation.  We find that mass accretion into corres tends to be episodic, and that the specific angular momentum doesn’t increase strongly with time as assumed in classical core models.  We further find that the directions of angular momenta are randomly oriented with respect to magnetic fields, and that cores are somewhat more magnetically-supercritical than often assumed.  These properties help to avoid the so-called “magnetic braking catastrophe”, in which magnetic fields carry off so much angular momentum during collapse that no protostellar disk forms.