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Star formation in our Galaxy occurs in molecular clouds that areself-gravitating, highly turbulent, and magnetized. We study the conditionsunder which cloud cores inherit large-scale magnetic field morphologies and howthe field is governed by cloud turbulence. We present four moving-meshsimulations of supersonic, turbulent, isothermal, self-gravitating gas with arange of magnetic mean-field strengths characterized by the Alfv\'enic Machnumber $\mathcal{M}_{{\rm A}, 0}$, resolving pre-stellar core formation fromparsec to a few AU scales. In our simulations with the turbulent kinetic energydensity dominating over magnetic pressure ($\mathcal{M}_{{\rm A}, 0}>1$), wefind that the collapse is approximately isotropic with $B\propto\rho^{2/3}$,core properties are similar regardless of initial mean-field strength, and thefield direction on $100$ AU scales is uncorrelated with the mean field.However, in the case of a dominant large-scale magnetic field($\mathcal{M}_{{\rm A}, 0}=0.35$), the collapse is anisotropic with$B\propto\rho^{1/2}$. This transition at $\mathcal{M}_{{\rm A}, 0}\sim1$ is notexpected to be sharp, but clearly signifies two different paths for magneticfield evolution in star formation. Based on observations of different starforming regions, we conclude that star formation in the interstellar medium mayoccur in both regimes. Magnetic field correlation with the mean-field extendsto smaller scales as $\mathcal{M}_{{\rm A}, 0}$ decreases, making future ALMAobservations useful for constraining $\mathcal{M}_{{\rm A}, 0}$ of theinterstellar medium.

Moving mesh simulations of star forming cores in magneto-gravo-turbulence