Magnetic diffusion in accretion flows changes the structure and angular momentum of the accreting material. We present two power law similarity solutions for flattened accretion flows in the presence of magnetic diffusion: a secularly-evolving Keplerian disc and a magnetically-diluted free fall onto the central object. The influence of Hall diffusion on the solutions is evident even when this is small compared to ambipolar and Ohmic diffusion, as the surface density, accretion rate and angular momentum in the flow all depend upon the product eta_H(B.Omega), and the inclusion of Hall diffusion may be the solution to the magnetic braking catastrophe of star formation simulations.
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