  The hot inner flow in black-hole X-ray binaries is not just a static corona
rotating around the black hole, but it must be partially outflowing. We have
developed a model, in which Comptonization takes place in this outflowing
corona. We are able to reproduce quantitatively five observed correlations: a)
the time lag as a function of Fourier frequency, b) the time lag as a function
of photon energy, c) the time lag as a function of $\Gamma$, d) the time lag as
a function of the cut-off energy in the spectrum, and e) the long-standing
radio - X-ray correlation. All of them with only two parameters (optical depth
and width of the outflow), which vary in the same ranges for all the
correlations. Our model does not require a compact, narrow relativistic jet,
although its presence does not affect the results. The essential ingredient of
our model is the parabolic shape of the Comptonizing corona. The outflow speed
also plays a minor role. Furthermore, the bottom of the outflow, in the hard
state, looks like a ``slab'' to the incoming soft photons from the disk, and
this can explain the observed X-ray polarization, which is along the outflow.
