  We revisit the question of 'hot mode' versus 'cold mode' accretion onto
galaxies using steady-state cooling flow solutions and idealized 3D
hydrodynamic simulations. We demonstrate that for the hot accretion mode to
exist, the cooling time is required to be longer than the free-fall time near
the radius where the gas is rotationally-supported, R_circ, i.e. the existence
of the hot mode depends on physical conditions at the galaxy scale rather than
on physical conditions at the halo scale. When allowing for the depletion of
the halo baryon fraction relative to the cosmic mean, the longer cooling times
imply that a virialized gaseous halo may form in halo masses below the
threshold of ~10^12 M_sun derived for baryon-complete halos. We show that for
any halo mass there is a maximum accretion rate for which the gas is virialized
throughout the halo and can accrete via the hot mode of Mdot_crit ~ 0.7(v_c/100
km/s)^5.4 (R_circ / 10 kpc) (Z/Z_sun)^-0.9 M_sun / yr, where Z and v_c are the
metallicity and circular velocity measured at R_circ. For accretion rates
>~Mdot_crit the volume-filling gas phase can in principle be `transonic' --
virialized in the outer halo but cool and free-falling near the galaxy. We
compare Mdot_crit to the average star formation rate (SFR) in halos at 0<z<10
implied by the stellar-mass halo-mass relation. For a plausible metallicity
evolution with redshift, we find that SFR <~ Mdot_crit at most masses and
redshifts, suggesting that the SFR of galaxies could be primarily sustained by
the hot mode in halo masses well below the classic threshold of ~10^12 M_sun.
