[en] We study the interaction of an ultra-high intensity laser pulse with plastic nano-layered flat-top cone targets by performing particle-in-cell simulations. Also, we analyze the spatio-temporal dynamics of the electromagnetic field based on the finite-difference time-domain method in order to isolate the geometric effects which affect the incoming laser-plasma interaction. We consider an ultra-high intensity laser pulse with linear and circular polarization. We have determined the optimum diameter of the nanospheres for a given nano-layer foil thickness for which it can be obtained beams of very energetic protons with low angular divergence. We point out that the protons are accelerated by a hybrid mechanism composed of target normal sheath acceleration and radiation pressure acceleration. This numerical study will allow to prepare and optimize first laser ion acceleration experiments on Extreme Light Infrastructure-Nuclear Physics and other PW laser facilities. (paper)