Abstract
We find exact and explicit self-similar solutions of the axisymmetric MHD equations of a self-gravitating polytropic gas. These solutions are able to describe a flat (uniform density) subsonic internal core, contracting homologously out of a collapsing cloud with aspherical pressure, aspherical gravitational potential, magnetic field and rotation. Two of the solutions describing the collapse of a rotating and magnetized cloud present outflow at the pole or at the equator.
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