We consider a 2D ballistic and quasi-ballistic structures with spin-orbit-related splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which arises in the presence of a charge current through the structure. We solve the problem with the use of the method of scattering states and clarify the important role of the unitarity of scattering. In the case of a straight boundary it leads to exact

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... ation of long-wavelength oscillations of the spin density. In general, however, the smooth spin oscillations with the spin precession length may arise, as it happens, e.g., for the wiggly boundary. Moreover, we show that the result crucially depends on the form of the spin-orbit Hamiltonian.