  We examine the effects of self-gravity and magnetic fields on supersonic
turbulence in isothermal molecular clouds with high resolution simulations and
adaptive mesh refinement. These simulations use large root grids (512^3) to
capture turbulence and four levels of refinement to capture high density, for
an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two
super-Alfv\'enic and one trans-Alfv\'enic. We find that gravity splits the
clouds into two populations, one low density turbulent state and one high
density collapsing state. The low density state exhibits properties similar to
non-self-gravitating in this regime, and we examine the effects of varied
magnetic field strength on statistical properties: the density probability
distribution function is approximately lognormal; velocity power spectral
slopes decrease with field strength; alignment between velocity and magnetic
field increases with field; the magnetic field probability distribution can be
fit to a stretched exponential. The high density state is characterized by
self-similar spheres; the density PDF is a power-law; collapse rate decreases
with increasing mean field; density power spectra have positive slopes,
P({\rho},k) \propto k; thermal-to-magnetic pressure ratios are unity for all
simulations; dynamic-to-magnetic pressure ratios are larger than unity for all
simulations; magnetic field distribution is a power-law. The high Alfv\'en Mach
numbers in collapsing regions explain recent observations of magnetic influence
decreasing with density. We also find that the high density state is found in
filaments formed by converging flows, consistent with recent Herschel
observations. Possible modifications to existing star formation theories are
explored.
