  In this paper we prove that the quotient of any real or complex moment-angle
complex by any closed subgroup in the naturally acting compact torus on it is
equivariantly homotopy equivalent to the homotopy colimit of a certain toric
diagram. For any quotient we prove an equivariant homeomorphism generalizing
the well-known Davis-Januszkiewicz construction for quasitoric manifolds and
small covers. We deduce formality of the corresponding Borel construction space
under the natural assumption on the group action in the complex case leading to
the new description of the equivariant cohomology for the quotients by any
coordinate subgroups. We prove the weak Toral Rank Conjecture for any partial
quotient by the diagonal circle action. We give an explicit construction of
partial quotients by circle actions having arbitrary torsion in integral
cohomology.
