In this contribution, we investigate the system of magnetic shifted dipoles using molecular dynamics simulations to elucidate the subject. We present an extensive study of the cluster formation in these systems both in three and two dimensions. It is shown that the more the dipole moment is shifted away from the particle centre the stronger it influences the microstructure of the system, both at low and room temperature. For larger shifts, the dimensionality of the system does not influence much the cluster structure.