  We have recently introduced in paper I an extension of the
Ruffini-Arg\"uelles-Rueda (RAR) model for the distribution of DM in galaxies,
by including for escape of particle effects. Being built upon self-gravitating
fermions at finite temperatures, the RAR solutions develop a characteristic
\textit{dense quantum core-diluted halo} morphology which, for fermion masses
in the range $mc^2 \approx 10-345$ keV, was shown to provide good fits to the
Milky Way rotation curve. We study here for the first time the applicability of
the extended RAR model to other structures from dwarfs to ellipticals to galaxy
clusters, pointing out the relevant case of $mc^2 = 48$ keV. By making a full
coverage of the remaining free parameters of the theory, and for each galactic
structure, we present a complete family of astrophysical RAR profiles which
satisfy realistic halo boundary conditions inferred from observations. Each
family-set of RAR solutions predicts given windows of total halo masses and
central quantum-core masses, the latter opening the interesting possibility to
interpret them as alternatives either to intermediate-mass BHs (for dwarf
galaxies), or to supermassive BHs (SMBHs, in the case of larger galaxy types).
The model is shown to be in good agreement with different observationally
inferred scaling relations such as: (1) the Ferrarese relation connecting DM
halos with supermassive dark central objects; and (2) the nearly constant DM
surface density of galaxies. Finally, the theory provides a natural mechanism
for the formation of SMBHs of few $10^8 M_\odot$ via the gravitational collapse
of unstable DM quantum-cores.
