  Motivated by the centering of biological objects in large cells, we study the
generic properties of centering forces inside a ball (or a volume of spherical
topology) in $n$ dimensions. We consider two scenarios : autonomous centering
(in which distance information is integrated from the agent perspective) and
non-autonomous centering (in which distance to the surface is integrated over
the whole surface). We find relations between the net centering force and the
mean distance$^p$ to the surface. This allows us to find simple scaling laws
between the centering force and the distance to the center, as a function of
the dimensionality $n$. Interestingly, if the interactions between the agent
and the surface are hyper-elastic, the net centering force can still be
sub-elastic in the case of autonomous centering. These scaling laws are
increasingly violated as the space becomes less convex. Generically, neither
scenarios exactly converge to the center of mass of the space.
