We study one dimensional dipole cascade models in the high-energy limit of QCD. Motivated by data on hadron multiplicities in the LHCb kinematical range, we generalize existing cascade models for splitting and recombination to account also for transitions to the vacuum. This modification allows us to describe the data. Furthermore, we perform both analytical and numerical studies of the cascades and find that the cascade including loop corrections, as well as the one accounting for transitions to the vacuum, can both be related to the Negative Binomial Distribution. In the latter case, however, one must properly normalize the cascade to account for transitions to the vacuum. We also study the scaling properties of the cascades and identify new regimes, which we call “focal” and “parallel.” Finally, we investigate the Quantum Information (QI) measures of the cascades, which allow us to highlight their distinctive properties.