  Let N be a manifold (with boundary) of dimension at least 3, such that its
interior admits a hyperbolic metric of finite volume. We discuss the possible
limits arising from sequences of relative fundamental cycles approximating the
simplicial volume.
  As applications, we extend results of Jungreis and Calegari from closed
hyperbolic to finite-volume hyperbolic manifolds: a) strict subadditivity of
simplicial volume with respect to isometric glueing along geodesic surfaces,
and b) nontriviality of the foliated Gromov norm for "most" foliations with
two-sided branching.
