  Transport and non-equilibrium magnetization in monolayers of magnetic
molecules subject to a bias voltage are considered. We apply a master-equation
approach going beyond the sequential-tunneling approximation to study the
Coulomb-blockade regime. While the current is very small in this case, the
magnetization shows changes of the order of the saturation magnetization for
small variations of the bias voltage. Inelastic cotunneling processes manifest
themselves as differential-conductance steps, which are accompanied by much
larger changes in the magnetization. In addition, the magnetization in the
Coulomb-blockade regime exhibits strong signatures of sequential tunneling
processes de-exciting molecular states populated by inelastic cotunneling. We
also consider the case of a single molecule, finding that cotunneling processes
lead to the occurrence of magnetic sidebands below the Coulomb-blockade
threshold. In the context of molecular electronics, we study how additional
spin relaxation suppresses the fine structure in transport and magnetization.
