  In this work we present for the first time predictions for top-quark pair
differential distributions at the LHC at NNLO QCD accuracy and including EW
corrections. For the latter we include not only contributions of ${\cal
O}(\alpha_s^2 \alpha)$, but also those of order ${\cal O}(\alpha_s \alpha^2)$
and ${\cal O}( \alpha^3)$. Besides providing phenomenological predictions for
all main differential distributions with stable top quarks, we also study the
following issues. 1) The effect of the photon PDF on top-pair spectra: we find
it to be strongly dependent on the PDF set used -- especially for the top $p_T$
distribution. 2) The difference between the additive and multiplicative
approaches for combining QCD and EW corrections: with our scale choice, we find
relatively small differences between the central predictions, but reduced scale
dependence within the multiplicative approach. 3) The potential effect from the
radiation of heavy bosons on inclusive top-pair spectra: we find it to be,
typically, negligible.
