  We briefly review the problem of generating cosmological flows of matter in
GR (the genesis of universes), analyze models' shortcomings and their basic
assumptions yet to be justified in physical cosmology. We propose a paradigm of
cosmogenesis based on the class of spherically symmetric solutions with {\it
integrable} singularity $r=0$. They allow for geodesically complete geometries
of black/white holes, which may comprise space-time regions with properties of
cosmological flows.
