Abstract. In contrast to the way that the spreading of irregularities in a plasma is usually considered, the diffusion spreading of irregularities stretched along the geomagnetic field B is examined using a three-dimensional rigorous numerical model of quasi-neutral diffusion in the presence of a magnetic field, in conjunction with the actual height variations of the diffusion and conductivity tensors in the ionosphere. A comparison with the earlier constructed approximate model of unipolar diffusion was made. As in the previous case, the same peculiarities of irregularity spreading in the inhomogeneous background ionospheric plasma were observed. The accuracy of the approximate model for describing the process of spreading of anisotropic ionospheric irregularities is established. Time relaxation effects of real heating-induced ionospheric irregularities on their scale transverse to B are presented using the approximate analytical model for the case of a quasi-homogeneous ionospheric plasma. The calculated results have a vivid physical meaning and can be directly compared with experimental data on the radiophysical observations of artificial heating-induced irregularities created by powerful radio waves in the ionosphere.