  Magnetic fields play an important role in star formation by regulating the
removal of angular momentum from collapsing molecular cloud cores. Hall
diffusion is known to be important to the magnetic field behaviour at many of
the intermediate densities and field strengths encountered during the
gravitational collapse of molecular cloud cores into protostars, and yet its
role in the star formation process is not well-studied. We present a
semianalytic self-similar model of the collapse of rotating isothermal
molecular cloud cores with both Hall and ambipolar diffusion, and similarity
solutions that demonstrate the profound influence of the Hall effect on the
dynamics of collapse.
  The solutions show that the size and sign of the Hall parameter can change
the size of the protostellar disc by up to an order of magnitude and the
protostellar accretion rate by fifty per cent when the ratio of the Hall to
ambipolar diffusivities is varied between -0.5 <= eta_H / eta_A <= 0.2. These
changes depend upon the orientation of the magnetic field with respect to the
axis of rotation and create a preferred handedness to the solutions that could
be observed in protostellar cores using next-generation instruments such as
ALMA.
  Hall diffusion also determines the strength and position of the shocks that
bound the pseudo and rotationally-supported discs, and can introduce subshocks
that further slow accretion onto the protostar. In cores that are not initially
rotating Hall diffusion can even induce rotation, which could give rise to disc
formation and resolve the magnetic braking catastrophe. The Hall effect clearly
influences the dynamics of gravitational collapse and its role in controlling
the magnetic braking and radial diffusion of the field merits further
exploration in numerical simulations of star formation.
