Propagation of short and ultraintense laser pulses in a semi-infinite space of overdense hydrogen plasma is analyzed via fully relativistic, real geometry particle-in-cell (PIC) simulations including radiation friction. The relativistic transparency and hole-boring regimes are found to be sensitive to the transverse plasma field, backward light reflection, and laser pulse filamentation. For laser intensities approaching I ∼ 1024 W/cm2, the direct laser acceleration of protons, along with ion Coulomb explosion, results in their injection into the acceleration phase of the compressed electron wave at the front of the laser pulses. The protons are observed to be accelerated up to 10–20 GeV with densities around a few times the critical density. The effect qualitatively depends on initial density and laser intensity, disappearing with the initial density increase or intensity decrease.