  We present predictions for the production cross section of a Standard Model
Z0-boson in association with a top-antitop pair at the next-to-leading order
accuracy in QCD, matched with shower Monte Carlo programs to evolve the system
down to the hadronization energy scale. We adopt a framework based on three
well established numerical codes, namely the POWHEG-BOX, used for computing the
cross section, HELAC-NLO, which generates all necessary input matrix elements,
and finally a parton shower program, such as PYTHIA or HERWIG, which allows for
including t-quark and Z0-boson decays at the leading order accuracy and
generates shower emissions, hadronization and hadron decays.
