  We calculate a comprehensive set of spin correlations and differential
distributions in top-quark pair production and decay to dilepton final states.
This is the first time such a complete study is performed at next-to-next-to
leading order in QCD. Both inclusive and fiducial distributions are presented
and analyzed. Good agreement between NNLO QCD predictions and data is found. We
demonstrate that it is possible to perform high-precision comparisons of
fixed-order calculations with fiducial-level data. Subtleties of the top quark
definition are raised and clarified. Some of those are found to have a very
significant impact on top-quark pair production at absolute threshold.
