  A point is called generic for a flow preserving an infinite ergodic invariant
Radon measure, if its orbit satisfies the conclusion of the ratio ergodic
theorem for every pair of continuous functions with compact support and
non-zero integrals. The generic points for horocycle flows on hyperbolic
surfaces of finite genus are understood, but there are no results in infinite
genus. We give such a result, by characterizing the generic points for
$\Z^d$--covers.
