  We investigate three-dimensional (3D) Anti-de Sitter (AdS) gravity coupled to
a complex scalar field \phi with self-interaction potential V(|\phi|). We show
that the mass of static, rotationally symmetric, AdS black hole with scalar
hairs is determined algebraically by the scalar charges. We recast the field
equations as a linear system of first order differential equations. Exact
solutions, describing 3D AdS black holes with real spherical scalar hairs and
vortex-black hole solutions are derived in closed form for the case of a scalar
field saturating the Breitenlohner-Freedman (BF) bound and for a scalar field
with asymptotic zero mass. The physical properties of these solutions are
discussed. In particular, we show that the vortex solution interpolates between
two different AdS_{3} vacua, corresponding respectively to a
U(1)-symmetry-preserving maximum and to a symmetry-breaking minimum of the
potential V.
