th} ^{\rm max}\simeq$ a few $\times 10^{53}$ ergs. However, the fraction of the thermal energy that is converted into the energy of the electron-positron fireball and then into the kinetic energy of the relativistic shell is very small and cannot be essentially more than $10^{-3}-10^{-2}$ ([@GDN]; [@Eichler89]; [@JR]; [@Piran98] and references therein). Moreover, the efficiency of transformation of the kinetic energy of a relativistic shell into radiation cannot be more than $30-40$% ([@be]). Hence, neutrino powered winds outflowing from compact objects may be responsible for the radiation of cosmological GRBs only if they are well collimated, with opening angle about a few degrees or even less. For both young neutron stars and post-merger objects, such a collimation of neutrino powered winds is very questionable (e.g., [@Woosley93]; [@Piran98] and references therein).

The rotational energy of the compact objects at the moment of their formation may be comparable with the thermal energy, $Q_{\rm rot}
^{\rm max}\simeq  Q_{\rm th} ^{\rm max}$. The efficiency of transformation of the rotational energy to the energy of a relativistic strongly magnetized wind and then to the energy of high-frequency radiation may be as high as almost 100% (see Usov 1994a,b; Blackman et al. 1996 and below). For 