  The observed slope at the high-mass end of the initial mass function (IMF)
displays a remarkable universality in a wide variety of physical environments.
We predict that competitive accretion, the ongoing accretion of gas from a
common reservoir by a collection of protostellar cores, can provide a natural
explanation for such a universal slope in star forming regions with
metallicities roughly greater than 1e-5 the solar value. In our discussion, we
point out that competitive accretion will occur whenever a gaseous region has
multiple Jeans masses of material and contains large-scale motions that are
controlled by the gravitational potential well. We describe how and when these
conditions can be reached during the chemical enrichment of the Universe,
showing that they can occur for a wide range of metallicities and environmental
conditions. We also discuss the ability of other physical processes to limit
the effects of further accretion onto protostellar cores. Current theoretical
and numerical studies show that competitive accretion is robust against
disrupting effects - such as feedback from young stars, supersonic turbulence
and magnetic fields - in all but the most extreme cases.
