  We investigate parton-branching methods based on transverse-momentum
dependent (TMD) parton distributions and matrix elements for the Monte Carlo
simulation of multi-particle final states at high-energy colliders. We observe
that recently measured angular correlations in ep final states with multiple
hadronic jets probe QCD coherence effects in the space-like branching,
associated with finite-angle gluon radiation from partons carrying small
longitudinal momenta, and not included in standard shower generators. We
present Monte Carlo calculations for azimuthal two-jet and three-jet
distributions, for jet multiplicities and for correlations in the
transverse-momentum imbalance between the leading jets. We discuss comparisons
with current experimental multi-jet data, and implications of corrections to
collinear-ordered showers for LHC final states.
