  The oxygen deficient CuO_x planes of the high-Tc superconductors
REBa_2Cu_3O_{6+x} (RE denotes a rare-earth atom or yttrium) are studied.
Starting from the Emery model for the Cu-O chain fragments, an extended ASYNNNI
model is proposed to describe the statistical mechanics of the CuO_x planes.
The model is analysed by using Monte Carlo techniques, computing especially the
charge transfer to the CuO$_2$ planes regulating the high-Tc superconductivity,
and the concentration of differently coordinated Cu ions.Results are compared
to experimental data for various RE cases.
