  This paper re-examines the problem of ambipolar diffusion as a mechanism for
the production and runaway evolution of centrally condensed molecular cloud
cores, a process that has been termed the gravomagneto catastrophe. Our
calculation applies in the geometric limit of a highly flattened core and
allows for a semi-analytic treatment of the full problem, although physical
fixes are required to resolve a poor representation of the central region. A
noteworthy feature of the overall formulation is that the solutions for the
ambipolar diffusion portion of the evolution for negative times ($t < 0$) match
smoothly onto the collapse solutions for positive times ($t > 0$). The
treatment shows that the resulting cores display non-zero, but
sub-magnetosonic, inward velocities at the end of the diffusion epoch, in
agreement with current observations. Another important result is the derivation
of an analytic relationship between the dimensionless mass to flux ratio
$\lambda_0\equiv f_0^{-1}$ of the central regions produced by runaway core
condensation and the dimensionless measure of the rate of ambipolar diffusion
$\epsilon$. In conjunction with previous work showing that ambipolar diffusion
takes place more quickly in the presence of turbulent fluctuations, i.e., that
the effective value of $\epsilon$ can be enhanced by turbulence, the resultant
theory provides a viable working hypothesis for the formation of isolated
molecular-cloud cores and their subsequent collapse to form stars and planetary
systems.
