The main result of this paper is an effective count for Apollonian circle
packings that are either bounded or contain two parallel lines. We obtain this
by proving an effective equidistribution of closed horospheres in the unit
tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite
volume, whose fundamental group has critical exponent bigger than 1. We also
discuss applications to Affine sieves. Analogous results for surfaces are
treated as well.Comment: 43 pages, 2 figures, To appear in GAF