  We present a model for a corona above a geometrically thin standard disk
around a black hole. This corona is fed by matter from the thin disk which
evaporates from the cool layers underneath. An equilibrium establishes between
the cool accretion stream and the hot flow. In the inner region evaporation
becomes so efficient that at low accretion rates all matter flows via the
corona and proceeds towards the black hole as an advection-dominated accretion
flow (ADAF). We investigate this transition for accretion disks around stellar
black holes. We derive a set of four ordinary differential equations which
describe the relevant processes and solve them numerically. The evaporation
efficiency has a maximum value where the advection-dominated structure of the
corona (at large distances from the black hole) changes to a
radiation-dominated structure (at small distances). This maximum can be related
to the observed spectral transitions in black hole X-ray binaries. Our
solutions of coronal structure are valid for both, accretion in galactic X-ray
transients and in AGN.
