  For growing inhomogeneous thin films with an island nanostructure similar as
observed in experiment, we determine the nonequilibrium and equilibrium
remanent magnetization. The single-island magnetic anisotropy, the dipole
coupling, and the exchange interaction between magnetic islands are taken into
account within a micromagnetic model. A cluster Monte Carlo method is developed
which includes coherent magnetization changes of connected islands. This causes
a fast relaxation towards equilibrium for irregularly connected systems. We
analyse the transition from dipole coupled islands at low coverages to a
strongly connected ferromagnetic film at high coverages during film growth. For
coverages below the percolation threshold, the dipole interaction induces a
collective magnetic order with ordering temperatures of 1 - 10 K for the
assumed model parameters. Anisotropy causes blocking temperatures of 10 - 100 K
and thus pronounced nonequilibrium effects. The dipole coupling leads to a
somewhat slower magnetic relaxation.
