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The equilibrium configurations of films consisting of magnetic small particles in which the anisotropy energy tends to align the magnetic moments perpendicular to the film are studied by Monte Carlo simulations. The effects of anisotropy energy, dipolar interaction, and Zeeman energy due to an external applied magnetic field, which can either be perpendicular or parallel to the film, are considered. As the relative strength of the relevant interaction energies changes, the system exhibits a variety of different magnetic moment configurations. Due to the competition between the dipolar interaction energy and the anisotropy energy, it is found that an approximately antiferromagnetic alignment with moments oriented perpendicular to the film results when the anisotropy energy dominates; while an in-plane antiferromagnetic alignment results when the dipolar interaction energy dominates. Results obtained by a zero-temperature analysis based on energy minimization are found to be in qualitative agreement with results obtained by numerical simulations.