By a systematic method we construct general classes of exact and self-consistent axisymmetric magnetohydrodynamic (MHD) solutions describing flows that originate in the near environment of a central gravitating astrophysical object. The unifying scheme contains two large groups of exact MHD outflow models: (I) meridionally self-similar models with spherical critical surfaces; and (II) radially self-similar models with conical critical surfaces. This classification includes known polytropic models, such as the classical Parker description of a stellar wind and the Blandford & Payne model of a disc wind; it also contains non-polytropic models, such as those of winds/jets in Sauty & Tsinganos, Lima, Tsinganos & Priest, and Trussoni, Tsinganos & Sauty. Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analysed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized and rotating astrophysical objects in stellar or galactic systems.
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Vlahakis et al. (1998) studied this question.