In this work we will explore the properties of superconducting surfaces
decorated by two-dimensional ferromagnetic adatom lattices. As discovered
recently [R\"ontynen and Ojanen, Phys. Rev. Lett. \textbf{114}, 236803 (2015)],
in the presence of a Rashba spin-orbit coupling these systems may support
topological superconductivity with complex phase diagrams and high Chern
numbers. We show how the long-range hopping nature of the effective low-energy
theory generically gives rise to a phase diagram covered by a \emph{Chern
mosaic} -- a rich pattern of topological phases with large Chern numbers. We
study different lattice geometries and the dependence of energy gaps and
abundance of different phases as a function of system parameters. Our findings
establish the studied system as one of the richest platforms for topological
matter known to date.Comment: 9 pages, 8 figure
