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 mu m) 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 similar to(2-5) x 10(20)W/cm(2) irradiating the target of the areal proton density similar to 2 x 10(20)cm(-2) 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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3590856]