  Parabolic fixed points form a countable dense subset of the limit set of a
non-elementary geometrically finite Kleinian group with at least one parabolic
element. Given such a group, one may associate a standard set of pairwise
disjoint horoballs, each tangent to the boundary at a parabolic fixed point.
The diameter of such a horoball can be thought of as the `inverse cost' of
approximating an arbitrary point in the limit set by the associated parabolic
point. A result of Stratmann and Velani allows one to count horoballs of a
given size and, roughly speaking, for small $r>0$ there are $r^{-\delta}$ many
horoballs of size approximately $r$, where $\delta$ is the Poincar\'e exponent
of the group. We investigate localisations of this result, where we seek to
count horoballs of size approximately $r$ inside a given ball $B(z,R)$. Roughly
speaking, if $r \lesssim R^2$, then we obtain an analogue of the
Stratmann-Velani result (normalised by the Patterson-Sullivan measure of
$B(z,R)$). However, for larger values of $r$, the count depends in a subtle way
on $z$. Our counting results have several applications, especially to the
geometry of conformal measures supported on the limit set. For example, we
compute or estimate several `fractal dimensions' of certain $s$-conformal
measures for $s>\delta$ and use this to examine continuity properties of
$s$-conformal measures at $s=\delta$.
