  Exact calculations of collective excitations and charge/spin (pseudo)gaps in
an ensemble of bipartite and nonbipartite clusters yield level crossing
degeneracies, spin-charge separation, condensation and recombination of
electron charge and spin, driven by interaction strength, inter-site couplings
and temperature. Near crossing degeneracies, the electron configurations of the
lowest energies control the physics of electronic pairing, phase separation and
magnetic transitions. Rigorous conditions are found for the smooth and dramatic
phase transitions with competing stable and unstable inhomogeneities.
Condensation of electron charge and spin degrees at various temperatures offers
a new mechanism of pairing and a possible route to superconductivity in
inhomogeneous systems, different from the BCS scenario. Small bipartite and
frustrated clusters exhibit charge and spin inhomogeneities in many respects
typical for nano and heterostructured materials. The calculated phase diagrams
in various geometries may be linked to atomic scale experiments in high T$_c$
cuprates, manganites and other concentrated transition metal oxides.
