The structures of plasma flows in close binary systems whose accretors have strong intrinsic magnetic fields are studied. A close binary system with the parameters of a typical polar is considered. The results of three dimensional numerical simulations of the material flow from the donor into the accretor Roche lobe are presented. Special attention is given to the flow structure in the vicinity of the inner Lagrangian point, where the accretion flow is formed. The interaction of the accretion flow material from the envelope of the donor with the magnetic field of the accretor results in the formation of a hierarchical structure of the magnetosphere, because less dense areas of the accretion flow are captured by the magnetic field of the white dwarf earlier than more dense regions. Taking into account this kind of magnetosphere structure can affect analysis results and interpretation of the observations.

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