  Dense clouds of neutrinos and antineutrinos can exhibit fast collective
flavor oscillations. Previously, in Phys. Rev. Lett. 126 (2021) 061302, we
proposed that such flavor oscillations lead to depolarization, i.e., an
irreversible mixing of the flavors, whose extent depends on the initial
momentum distributions of the different flavors. In this paper, we elaborate
and extend this proposal, and compare it with related results in the
literature. We present an accurate analytical estimate for the lower resting
point of the fast flavor pendulum and underline the relaxation mechanisms,
i.e., transverse relaxation, multipole cascade, and mixing of flavor-waves,
that cause it to settle down. We estimate the extent of depolarization, its
dependence on momentum and net lepton asymmetry, and its generalization to
three flavors. Finally, we prescribe approximate analytical recipes for the
depolarized distributions and fluxes that can be used in
supernova/nucleosynthesis simulations and supernova neutrino phenomenology.
