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Measurements of charged-particle production in pp, p−Pb, and Pb−Pb collisions in the toward, away, and transverse regions with the ALICE detector are discussed. These regions are defined event-by-event relative to the azimuthal direction of the charged trigger particle, which is the reconstructed particle with the largest transverse momentum (ptrigT) in the range 8<ptrigT<15 GeV/c. The toward and away regions contain the primary and recoil jets, respectively; both regions are accompanied by the underlying event (UE). In contrast, the transverse region perpendicular to the direction of the trigger particle is dominated by the so-called UE dynamics, and includes also contributions from initial- and final-state radiation. The relative transverse activity classifier, RT=NTch/⟨NTch⟩, is used to group events according to their UE activity, where NTch is the charged-particle multiplicity per event in the transverse region and ⟨NTch⟩ is the mean value over the whole analysed sample. The energy dependence of the RT distributions in pp collisions at s√=2.76, 5.02, 7, and 13 TeV is reported, exploring the Koba-Nielsen-Olesen (KNO) scaling properties of the multiplicity distributions. The first measurements of charged-particle pT spectra as a function of RT in the three azimuthal regions in pp, p−Pb, and Pb−Pb collisions at sNN−−−√=5.02 TeV are also reported. Data are compared with predictions obtained from the event generators PYTHIA 8 and EPOS LHC. This set of measurements is expected to contribute to the understanding of the origin of collective-like effects in small collision systems (pp and p−Pb).