A study of the charged-particle density (number density) in the transverse region of the di-hadron correlations exploiting the existing pp and p$bar{rm p}$ data from RHIC to LHC energies is reported. This region has contributions from the Underlying Event (UE) as well as from Initial- and Final-State Radiation (ISR-FSR). Based on the data, a two-component model is built. This has the functional form $propto s^{0.27}+0.14log(s)$, where the logarithmic (power-law) term describes the component more sensitive to the ISR-FSR (UE) contribution. The model describes the data from RHIC to LHC energies, the extrapolation to higher energies indicates that at around $sqrt{s} approx 100$ TeV the number density associated to UE will match that from ISR-FSR. Although this behaviour is not predicted by PYTHIA~8.244, the power-law behaviour of the UE contribution is consistent with the energy dependence of the parameter that regulates Multiparton Interactions. Using simulations, KNO-like scaling properties of the multiplicity distributions in the regions sensitive to either UE or ISR-FSR are also discussed. The results presented here can be helpful to constrain QCD-inspired Monte Carlo models at the Future Circular Collider energies, as well as to characterize the UE-based event classifiers which are currently used at the LHC.
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