Let \(\Gamma\) be a cofinite Fuchsian group. Let \(z,w\) be points of the hyperbolic plane. We denote by \(n_t(z,w)\) the number of elements of \(\Gamma z\) (counted with multiplicity) in a ball of radius \(t\) around \(w\). The author proves in this paper two theorems which describe the asymptotic behaviour of \(n_t(z,w)\) in its dependence on \(z,w\). The first of the two theorems is a point-wise estimate which follows from a covering argument and an estimate of Iwaniec. The second estimate is integrated over \(t\) and requires new estimates of the contribution from the spectral expansion. This is achieved by the choice of a Selberg kernel whose Selberg transform can, with some effort, be estimated in such a useful fashion. Finally the author applies these results to study interpolation in weighted Bergman spaces.