In this paper, we present a detailed investigation of the impact of fin width (w(fin)) on tri-gate AlGaN/GaN metal-oxide-semiconductor high electron mobility transistors (MOSHEMTs). As w(fin) is reduced, the threshold voltage (V-TH) increases, which is due to the enhanced gate control (especially for w(fin) < 200 nm) thanks to the 3-D geometry of the tri-gate, and the reduced carrier concentration (N-s) caused by a more pronounced strain relaxation and sidewall depletion, as explored using Hall and capacitance-voltage (C-V) measurements. Normally-OFF operation was achieved for wfin close to the sidewall depletion width (w(dep)) of 19.5 nm, since the fin is depleted from its two sidewalls. The impact of w(fin) on ON-resistance (R-ON) and current capability (I-D,I- max) was also investigated, along with the influence of the effective source injection, the trench conduction and the filling factor (FF) on these key characteristics. The degradation caused by the tri-gate fin etching could be fully recovered by increasing the FF. Finally, we show that the tri-gate can reduce gate capacitance (C-G) and charge (Q(G)) in normally-ON MOSHEMTs, depending on the design of the tri-gate and the gate voltage (V-G), leading to a smaller R-ON . Q(G) product that is beneficial for high-frequency switching applications. The results in this paper offer insights into important phenomena in tri-gate GaN devices and are fundamental for the further advance of this technology.