  A wide class of non-stationary superdiffusive transport on a uniform
background with a power-law decay, at large distances, of the step-length
probability distribution function (PDF) is shown to possess an automodel
solution. The solution for Green function is constructed using the scaling laws
for the propagation front (relevant-to-superdiffusion average displacement) and
asymptotic solutions far beyond and far in advance of the propagation front.
These scaling laws are determined essentially by the long-free-path carriers
(L\'evy flights). The validity of the suggested automodel solution is proved by
its comparison with numerical solutions in the one-dimensional (1D) case of the
transport equation with a simple long-tailed PDF with various power-law
exponents and in the 3D case of the Biberman-Holstein equation of the resonance
radiation transfer for various (Doppler, Lorentz, Voight and Holtsmark)
spectral line shapes.
