  We find exact and explicit 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, of a
collapsing cloud with aspherical pressure, aspherical gravitationnal 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.
