  Line-driven winds from stars and accretion disks are accelerated by
scattering in numerous line transitions. The wind is believed to adopt a unique
critical solution, out of the infinite variety of shallow and steep solutions.
We study the inherent dynamics of the transition towards the critical wind. A
new runaway wind mechanism is analyzed in terms of radiative-acoustic (Abbott)
waves which are responsible for shaping the wind velocity law and fixing the
mass loss. Three different flow types result, depending on the location of
perturbations. First, if the shallow solution is perturbed sufficiently far
downstream, a single critical point forms in the flow, which is a barrier for
Abbott waves, and the solution tends to the critical one. Second, if the
shallow solution is perturbed upstream from this critical point, mass
overloading results, and the critical point is shifted inwards. This wind
exhibits a broad, stationary region of decelerating flow and its velocity law
has kinks. Third, for perturbations even further upstream, the overloaded wind
becomes time-dependent, and develops shocks and dense shells.
