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 (5123) to capture turbulence and four levels of refinement to follow the collapse to high densities, for an effective resolution of 81923. Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. 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, the velocity power spectral slopes decrease with decreasing mean field strength, the alignment between velocity and magnetic field increases with the field, and the magnetic field probability distribution can be fitted to a stretched exponential. The high-density state is well characterized by self-similar spheres: the density probability distribution is a power law, collapse rate decreases with increasing mean field, density power spectra have positive slopes, P(ρ, k)∝k, thermal-to-magnetic pressure ratios are roughly unity for all mean field strengths, dynamic-to-magnetic pressure ratios are larger than unity for all mean field strengths, the magnetic field distribution follows a power-law distribution. The high Alfvén Mach numbers in collapsing regions explain the recent observations of magnetic influence decreasing with density. We also find that the high-density state is typically found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored. The overall trans-Alfvénic nature of star-forming clouds is discussed.
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