  We consider constellations of disks which are unions of disjoint hyperbolic
disks in the unit disk with fixed radii and unfixed centers. We study the
problem of maximizing the conformal capacity of a constellation under
constraints on the centers in two cases. In the first case the constraint is
that the centers are at most at distance $R \in(0,1)$ from the origin and in
the second case it is required that the centers are on the subsegment $[-R,R]$
of a diameter of the unit disk. We study also similar types of constellations
with hyperbolic segments instead of the hyperbolic disks. Our computational
experiments suggest that a dispersion phenomenon occurs: the disks/segments go
as close to the unit circle as possible under these constraints and stay as far
as possible from each other. The computation of capacity reduces to the
Dirichlet problem for the Laplace equation which we solve with a fast boundary
integral equation method. The results are double-checked with the $hp$-FEM
method.
