  We map out the QCD phase structure at finite temperature and chemical
potential for 2-flavour and 2 + 1-flavour QCD. This is done within a
generalised functional approach to QCD put forward in arXiv:2002.07500
[hep-ph]. Specifically we compute the quark propagator and the
finite-temperature and density fluctuations of the gluon propagator and the
quark-gluon vertex on the basis of precision data for vacuum correlation
functions. The novel ingredient is the direct self-consistent computation of
the DSEs for the dressings of the quark-gluon vertex, in contrast to the common
use of STI-inspired vertices.
  For small densities the results for the chiral order parameter agree with the
respective lattice and functional renormalisation group results, for large
densities the present results are in a quantitative agreement with the latter,
including the location of the critical end point.
