  The formation and collapse of a protostar involves the simultaneous infall
and outflow of material in the presence of magnetic fields, self-gravity, and
rotation. We use self-similar techniques to self-consistently model the
anisotropic collapse and outflow by a set of angle-separated self-similar
equations. The outflow is quite strong in our model, with the velocity
increasing in proportion to radius, and material formally escaping to infinity
in the finite time required for the central singularity to develop.
  Analytically tractable collapse models have been limited mainly to
spherically symmetric collapse, with neither magnetic field nor rotation. Other
analyses usually employ extensive numerical simulations, or either perturbative
or quasistatic techniques. Our model is unique as an exact solution to the
non-stationary equations of self-gravitating MHD, which features co-existing
regions of infall and outflow.
  The velocity and magnetic topology of our model is quadrupolar, although
dipolar solutions may also exist. We provide a qualitative model for the origin
and subsequent evolution of such a state. However, a central singularity forms
at late times, and we expect the late time behaviour to be dominated by the
singularity rather than to depend on the details of its initial state. Our
solution may, therefore, have the character of an attractor among a much more
general class of self-similarity.
