  We develop an analytic framework to understand fragmentation in turbulent,
self-gravitating media. Previously, we showed some properties of turbulence can
be predicted with the excursion-set formalism. Here, we generalize to fully
time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent
systems are always gravitationally unstable (in a probabilistic sense). The
fragmentation mass spectra, size/mass relations, correlation functions, range
of scales over which fragmentation occurs, & time-dependent rates of
fragmentation are predictable. We show how this depends on bulk turbulent
properties (Mach numbers & power spectra). We also generalize to include
rotation, complicated equations of state, collapsing/expanding backgrounds,
magnetic fields, intermittency, & non-normal statistics. We derive how
fragmentation is suppressed with 'stiffer' equations of state or different
driving mechanisms. Suppression appears at an 'effective sonic scale' where
Mach(R,rho)~1. Gas becomes stable below this scale for polytropic gamma>4/3,
but fragmentation still occurs on larger scales. The scale-free nature of
turbulence and gravity generically drives mass spectra and correlation
functions towards universal shapes, with weak dependence on many properties of
the media. Correlated fluctuation structures, non-Gaussian density
distributions, & intermittency have surprisingly small effects on the
fragmentation process. This is because fragmentation cascades on small scales
are 'frozen in' when large-scale modes push the 'parent' region above the
collapse threshold; though they collapse, their statistics are only weakly
modified by the collapse process. With thermal support, structure develops
'top-down' in time via fragmentation cascades; but strong rotational support
reverses this to 'bottom-up' growth via mergers & introduces a maximal
instability scale distinct from the Toomre scale.
