Interaction of relativistically strong laser pulses with under- and overdense plasmas is studied by 3D particle-in-cell simulations. We show that electrons in the underdense plasmas can be accelerated not only by the plasma wake field, but also by direct laser push in self-generated magnetic and electrostatic fields. These two mechanisms of acceleration manifest themselves in the electron energy spectra as two effective “temperatures.” We show that the fast electrons transport a significant part of the laser pulse power through the overdense plasma in the form of magnetized jets. We also find high collective stopping because of an anomalous resistivity of the plasma.