  We perform a detail theoretical study including decays and jet fragmentation
of all the important modes of the single top quark production and all basic
background processes at the upgraded Tevatron and LHC colliders. Special
attention was paid to the complete tree level calculation of the QCD fake
background which was not considered in the previous studies. Analysis of the
various kinematical distributions for the signal and backgrounds allowed to
work out a set of cuts for an efficient background suppression and extraction
of the signal. It was shown that the signal to background ratio after optimized
cuts could reach about 0.4 at the Tevatron and 1 at the LHC. The remaining
after cuts rate of the signal at the LHC for the $lepton+jets $ signature is
expected to be about 6.1 pb and will be enough to study the single top physics
even during the LHC operation at a low luminosity.
