  We say that a tiling separates discs of a packing in the Euclidean plane, if
each tile contains exactly one member of the packing. It is a known elementary
geometric problem to show that for each locally finite packing of circular
discs, there exists a separating tiling with convex polygons. In this paper we
show that this separating property remains true for circle packings on the
sphere and in the hyperbolic plane. Moreover, we show that in the Euclidean
plane circles are the only convex discs, whose packings with similar copies can
be always separated by polygonal tilings. The analogous statement is not true
on the sphere and it is not known in the hyperbolic plane.
