  In this paper a mean-field theory for the spin-liquid paramagnetic
non-superconducting phase of the p- and n-type High-$T_c$ cuprates is
developed. This theory applied to the effective $t-t'-t''-J^*$ model with the
{\it ab initio} calculated parameters and with the three-site correlated
hoppings. The static spin-spin and kinematic correlation functions beyond
Hubbard-I approximation are calculated self-consistently. The evolution of the
Fermi surface and band dispersion is obtained for the wide range of doping
concentrations $x$. For p-type systems the three different types of behavior
are found and the transitions between these types are accompanied by the
changes in the Fermi surface topology. Thus a quantum phase transitions take
place at $x=0.15$ and at $x=0.23$. Due to the different Fermi surface topology
we found for n-type cuprates only one quantum critical concentration, $x=0.2$.
The calculated doping dependence of the nodal Fermi velocity and the effective
mass are in good agreement with the experimental data.
