[en] Various magnetic textures in the CuO₂ planes of high-T_c superconductors are studied using the three-band Hubbard Hamiltonian. In particular, the electron and hole doping dependence is determined. The textures studied for a lattice of supercells consisting of 4x4 CuO₂ cells include an antiferromagnetic state (AF), a spiral-like state, a vortex-like state, as well as domain structures. The relative stability of the magnetic textures is determined by using the unrestricted Hartree-Fock approximation and the real space recursion method. At the critical doping concentration for the destruction of the AF state, we find that domain-like textures have the lowest energy for hole doping and the spiral- and domain-like textures have the lowest energy for electron doping. In general, we obtain that the doping effect is intrinsically asymmetrical for electron and hole doping: the antiferromagnetic state is less rapidly destroyed in the case of electron doping, in agreement with experimental results. (author)