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Cut-off lows (COLs) exhibit diverse structures and lifecycles, ranging from confined upper-tropospheric systems to deep, multi-level vortex structures. While COL climatologies are well documented, the mechanisms driving their deepening remain unclear. To bridge this gap, a novel track matching algorithm applied to ERA-Interim reanalysis investigates the vertical extent of Southern Hemisphere COLs. Composite analysis based on structure and eddy kinetic energy budget differentiates four COL categories: shallow, deep, weak, and strong, revealing similarities and disparities. Deep, strong COLs concentrate around Australia and the southwestern Pacific, peaking in autumn and spring, while shallow, weak COLs are more common in summer and closer to the Equator. Despite their differences, both contrasting types evolve energetically via anticyclonic Rossby wave breaking. The distinct roles of jet streams in affecting COL types are addressed: intense polar front jets correlate with more deep COLs, whereas stronger subtropical jets relate to fewer shallow COLs. The COL deepening typically occurs in the presence of a robust upstream polar front jet, which enhances ageostrophic flux convergence and baroclinic processes. The subtropical jet positively correlates with COL intensity but weakens when considering the seasonality, suggesting uncertainties in this relationship. Additionally, we highlight the significance of diabatic processes in COL deepening, addressing their misrepresentation in reanalysis and emphasizing the need for more observational and modelling studies to refine the energetic framework.