Bounded deviations in higher genus II: minimal laminations

This article follows and completes [arXiv:2511.14222], where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This second part deals with bounded deviations relative to geodesic minimal laminations that are not reduced to a closed geodesic. The combination of both articles generalises to the higher genus case most of the bounded deviations results already known for the torus.