  Locally conformal almost quasi-Sasakian manifolds set up a wide class of
almost contact metric manifolds containing several interesting subclasses.
Contact-complex Riemannian submersions whose total space belongs to each of the
considered classes are studied. In particular, the Chinea-Gonzalez class of the
fibres and the Gray-Hervella class of the base space are determined. The main
properties of the O'Neill invariants are stated. This allows discussing the
integrability of the horizontal distribution and the minimality of the fibres.
