We perform a detail theoretical study including decays and jet fragmentationof all the important modes of the single top quark production and all basicbackground processes at the upgraded Tevatron and LHC colliders. Specialattention was paid to the complete tree level calculation of the QCD fakebackground which was not considered in the previous studies. Analysis of thevarious kinematical distributions for the signal and backgrounds allowed towork out a set of cuts for an efficient background suppression and extractionof the signal. It was shown that the signal to background ratio after optimizedcuts could reach about 0.4 at the Tevatron and 1 at the LHC. The remainingafter cuts rate of the signal at the LHC for the $lepton+jets $ signature isexpected to be about 6.1 pb and will be enough to study the single top physicseven during the LHC operation at a low luminosity.
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