  Every geodesic current on a hyperbolic surface has an associated dual space.
If the current is a lamination, this dual embeds isometrically into a real
tree. We show that, in general, the dual space is a Gromov hyperbolic metric
tree-graded space, and express its Gromov hyperbolicity constant in terms of
the geodesic current. In the case of geodesic currents with no atoms and full
support, such as those coming from certain higher rank representations, we show
the duals are homeomorphic to the surface. We also analyze the completeness of
the dual and the properties of the action of the fundamental group of the
surface on the dual. Furthermore, we compare two natural topologies in the
space of duals.
