  We investigate equilibrium accretion flows dominated by $e^+ e^-$ pairs. We
consider one- and two-temperature accretion disk coronae above a thin disk, as
well as hot optically thin two-temperature accretion flows without an
underlying thin disk; we model the latter in the framework of
advection-dominated accretion flows (ADAFs). In all three cases we include
equipartition magnetic fields. We confirm the previous result that the
equilibrium density of pairs in two-temperature ADAFs is negligible; and show
that the inclusion of magnetic fields and the corresponding synchrotron cooling
reduces the pair density even further. Similarly, we find that pairs are
unimportant in two-temperature coronae. Even when the corona has significantly
enhanced heating by direct transfer of viscous dissipation in the thin disk to
the corona, the inefficient Coulomb coupling between protons and electrons acts
as a bottleneck and prevents the high compactness required for pair-dominated
solutions. Only in the case of a one-temperature corona model do we find
pair-dominated thermal equilibria. These pair-dominated solutions occur over a
limited range of optical depth and temperature.
