A scheme of generation of ultraintense proton beams relevant for proton fast ignition (PFI) which employs multi-ps, circularly polarized laser pulse irradiating a thick (≥ 10 μm) H-rich target is proposed and examined using one-dimensional particle-in cell-simulations. It is shown that a 5-ps laser pulse of intensity ~(2–5)x10²⁰W=cm² irradiating the target of the areal proton density ~2x10²⁰cm² can produce – with a high energetic efficiency – a proton beam (plasma block) of parameters (intensity, energy fluence, pulse duration, proton energy spectrum) close to those required for PFI. At a fixed total laser energy, the proton beam parameters can be controlled and fitted to the PFI requirements by changing the laser intensity (energy fluence) and=or the target thickness as well as by using a shaped (curved) target inserted into a guiding cone.