  We study analytically black holes pierced by a thin vortex in dilatonic
gravity for an arbitrary coupling of the vortex to the dilaton in an arbitrary
frame. We show that the horizon of the charged black hole supports the
long-range fields of the Nielsen-Olesen vortex that can be considered as black
hole hair for both massive and massless dilatons. We also prove that extremal
black holes exhibit a flux expulsion phenomenon for a sufficiently thick
vortex. We consider the gravitational back-reaction of the thin vortex on the
spacetime geometry and dilaton, and discuss under what circumstances the vortex
can be used to smooth out the singularities in the dilatonic C-metrics. The
effect of the vortex on the massless dilaton is to generate an additional
dilaton flux across the horizon.
