This paper presents for the first time a precise measurement of the production properties of the Z boson in the full phase space of the decay leptons. This is in contrast to the many previous precise unfolded measurements performed in the fiducial phase space of the decay leptons. The measurement is obtained from proton–proton collision data collected by the ATLAS experiment in 2012 at s=8 TeV at the LHC and corresponding to an integrated luminosity of 20.2 fb-1. The results, based on a total of 15.3 million Z-boson decays to electron and muon pairs, extend and improve a previous measurement of the full set of angular coefficients describing Z-boson decay. The double-differential cross-section distributions in Z-boson transverse momentum pT and rapidity y are measured in the pole region, defined as 80<mℓℓ<100 GeV, over the range |y|<3.6. The total uncertainty of the normalised cross-section measurements in the peak region of the pT distribution is dominated by statistical uncertainties over the full range and increases as a function of rapidity from 0.5–1.0% for |y|<2.0 to 2-7% at higher rapidities. The results for the rapidity-dependent transverse momentum distributions are compared to state-of-the-art QCD predictions, which combine in the best cases approximate N4LL resummation with N3LO fixed-order perturbative calculations. The differential rapidity distributions integrated over pT are even more precise, with accuracies from 0.2–0.3% for |y|<2.0 to 0.4–0.9% at higher rapidities, and are compared to fixed-order QCD predictions using the most recent parton distribution functions. The agreement between data and predictions is quite good in most cases.