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We study the distribution of non-discrete orbits of geometrically finitegroups in $\operatorname{SO}(n,1)$ acting on $\mathbb{R}^{n+1}$, and moregenerally on the quotient of $\operatorname{SO}(n,1)$ by a horosphericalsubgroup. Using equidistribution of horospherical flows, we obtain bothasymptotics for the distribution of orbits for the action of generalgeometrically finite groups, and we obtain quantitative statements withadditional assumptions.

Distribution of orbits of geometrically finite groups acting on null vectors