We present a detailed assessment of the dynamical pathways leading to the coalescence of compact objects in Globular Clusters (GCs) and Short Gamma-Ray Burst (SGRB) production. We consider primordial binaries, dynamically formed binaries (through tidal two-body and three-body exchange interactions) and direct impacts of compact objects (WD/NS/BH). We show that if the primordial binary fraction is small, close encounters dominate the production rate of coalescing compact systems. We find that

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... two dominant channels are the interaction of field NSs with dynamically formed binaries, and two-body encounters. We then estimate the redshift distribution and host galaxy demographics of SGRB progenitors, and find that GCs can provide a significant contribution to the overall observed rate. We have carried out hydrodynamical modeling of evolution of close stellar encounters with WD/NS/BH, and show that there is no problem in accounting for the energy budget of a typical SGRB. The particulars of each encounter are variable and lead to interesting diversity: the encounter characteristics are dependent on the impact parameter, in contrast to the merger scenario; the nature of the compact star itself can produce very different outcomes; the presence of tidal tails in which material falls back onto the central object at later times is a robust feature of these calculations, with the mass involved being larger than for binary mergers. It is thus possible to account generically in this scenario for a prompt episode of energy release, as well as for activity many dynamical time scales later (abridged).