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We analyse the associated production of Higgs and $Z$ boson via heavy-quarkloops at the LHC in the Standard Model and beyond. We first review the mainfeatures of the Born $2\to 2$ production, and in particular discuss thehigh-energy behaviour, angular distributions and $Z$ boson polarisation. Wethen consider the effects of extra QCD radiation as described by the $2 \to 3$loop matrix elements, and find that they dominate at high Higgs transversemomentum. We show how merged samples of 0-- and 1--jet multiplicities, matchedto a parton shower can provide a reliable description of differentialdistributions in $ZH$ production. In addition to the Standard Model study,results in a generic two-Higgs-doublet-model are obtained and presented for aset of representative and experimentally viable benchmarks for $Zh^0$, $ZH^0$and $ZA^0$ production. We observe that various interesting features appeareither due to the resonant enhancement of the cross-section or to interferencepatterns between resonant and non-resonant contributions.

Higgs and Z boson associated production via gluon fusion in the SM and the 2HDM