  We present details of a calculation of the cross section for hadronic
top-antitop production in next-to-leading order (NLO) QCD, including the decays
of the top and antitop into bottom quarks and leptons. This calculation is
based on matrix elements for \nu e e+ \mu- \bar{\nu}_{\mu}b\bar{b} production
and includes all non-resonant diagrams, interferences, and off-shell effects of
the top quarks. Such contributions are formally suppressed by the top-quark
width and turn out to be small in the inclusive cross section. However, they
can be strongly enhanced in exclusive observables that play an important role
in Higgs and new-physics searches. Also non-resonant and off-shell effects due
to the finite W-boson width are investigated in detail, but their impact is
much smaller than naively expected. We also introduce a matching approach to
improve NLO calculations involving intermediate unstable particles. Using a
fixed QCD scale leads to perturbative instabilities in the high-energy tails of
distributions, but an appropriate dynamical scale stabilises NLO predictions.
Numerical results for the total cross section, several distributions, and
asymmetries are presented for Tevatron and the LHC at 7 TeV, 8 TeV, and 14 TeV.
