  The breakdown of flux-freezing in molecular clouds and protostellar discs is
usually approximated by ambipolar diffusion at low densities or by resistive
diffusion at high densities. Here I discuss an intermediate regime in which the
Hall term in the conductivity tensor is significant, and the vector evolution
of the magnetic field -- and therefore the evolution of the system under
consideration -- is dramatically altered. Calculations of charged particle
abundances in dense gas in molecular clouds and protostellar discs demonstrate
that Hall diffusion is important over a surprisingly broad range of conditions.
