The surface low of a mature extra-tropical cyclone is often surmounted by a troposphere-spanning column of anomalously high potential vorticity (PV). In this study the growth and decay of such a PV-tower is traced for one major North Atlantic frontal-wave cyclone using the ECMWF analysis fields and adopting both Eulerian and Lagrangian frameworks. A tower's structure and composition relates intimately to the strength, scale and structure of the associated surface cyclone. It is shown that the tower comprised a vertical superposition of three elements: (A) a quasi-seclusion of stratospheric air extruded from an upper-level trough, (B) a mid-tropospheric layer of intermingled air from diverse sources, but with a substantial component originating from the system's cold front, and (C) a low-tropospheric layer of diabatically-induced PV that was linked to and originated from flow along a bent-back warm front. An examination of the tower's growth and decay helps identify the factors influencing the onset and rapidity of the cyclogenesis. There was first an in-phase development of a surface baroclinic wave with the precursor of element (A), and also the emergence of element (B) in the form of a low-level elongated band of PV aligned along the cold front. Thereafter a short period of rapid growth was marked by the appearance of a low-level band of PV along the warm front (element C), and it co-spiraled with and beneath the upper-level stratospheric intrusion (element A). Demise of the tower followed a loss of amplitude of its central portion and a loss of coherency aloft. Evidence of the modulating as opposed to the dominating influence of diabatic processes upon the cyclone's structure and strength is derived from consideration of: the tower's durable and ephemeral potential vorticity, the PV production along the warm front, and sets of model simulations of the event that selectively suppress diabatic PV production.