There is a growing compelling experimental evidence that a quantum complex matter scenario made of multiple electronic components, and competing quantum phases is needed to grab the key physics of high critical temperature (Tc) superconductivity in layered cuprates. While it is known that defects self-organization controls Tc, the mechanism remains an open issue. Here we focus on the theoretical prediction of the multi-band electronic structure and the formation of broken Fermi surfaces generated by the self-organization of oxygen interstitials Oi atomic wires in the spacer layers in HgBa2CuO4+y, La2CuO 4±δ and La2NiO 4±δ , by means of self-consistent Linear Muffin-Tin Orbital (LMTO) calculations. The electronic structure of a first phase of ordered Oi atomic wires and of a second glassy phase made of disordered Oi impurities have been studied through supercell calculations. We show the common features of the influence of Oi wires in the electronic structure in three type of materials. The ordering of Oi into wires lead to a separation of the electronic states between the Oi ensemble and the rest of the bulk. The wires formation produce first quantum confined localized states near the wire which coexist with second delocalized states in the Fermisurface (FS) of doped cuprates. In this new scenario for high Tc superconductivity, Kitaev wires with Majorana bound states are proximity-coupled to a 2D d-wave superconductor in cuprates.