  For convex co-compact hyperbolic manifolds $\Gamma\backslash
\mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies
$\delta_\Gamma< n/2$, we show that the high-frequency Eisenstein series
associated to a point $\xi$ "at infinity" concentrate microlocally on a measure
supported by (the closure of) the set of points in the unit cotangent bundle
corresponding to geodesics ending at $\xi$. The average in $\xi$ of these limit
measures equidistributes towards the Liouville measure.
