Thin films of dilute magnetic oxides often exhibit high-temperature ferromagnetism with magnetization curves of the form M ¿ M _s tanh (H/H ₀ ); the curves are practically anhysteretic and temperature-independent below room temperature. The absence of temperature-dependent coercivity indicates that the magnetization process is dominated by magnetic dipole interactions, not by magnetocrystalline anisotropy. In a model of ferromagnetic grain boundaries, H ₀ ¿ 0.14M ₀ , where M ₀ is the magnetization of the ferromagnetic regions. Quantitative analysis of more than 200 films of different oxides reveals that only a few percent of the volume of these films is magnetically ordered.