This paper examines magnetic structures of 1D and 2D magnetics with competing anisotropy, and compares them with 3D systems. Asperomagnetic short-range order phases in such systems are shown to develop at space dimensionality d ≥ 2. Magnetic structures and spin-orientation processes in a thin film with fluctuations of the anisotropy constant throughout its thickness are investigated. A phase diagram of such a film is plotted; the influence of boundary effects on magnetic structures arising in the film is analyzed.