  In the absence of direct kinematic measurements, the mass of an accreting
black hole is sometimes inferred from the X-ray spectral parameters of its
accretion disk; specifically, from the temperature and normalization of a
disk-blackbody model fit. Suitable corrections have to be introduced when the
accretion rate approaches or exceeds the Eddington limit. We summarize
phenomenological models that can explain the very high state, with apparently
higher disk temperatures and lower inner-disk radii. Conversely, ultraluminous
X-ray sources often contain cooler disks with large characteristic radii. We
introduce another phenomenological model for this accretion state. We argue
that a standard disk dominates the radiative output for radii larger than a
characteristic transition radius R_c ~ mdot x R_{ISCO}, where mdot is the
accretion rate in Eddington units and R_{ISCO} is the innermost stable orbit.
For R_{ISCO} < R < R_c, most of the accretion power is released via non-thermal
processes. We predict the location of such sources in a luminosity-temperature
plot. We conclude that black holes with masses ~ 50-100 Msun accreting at mdot
~ 10-20 may explain the X-ray properties of many ULXs.
