<p class="p1">Tsunamis generated by gravitational flows at volcanic islands pose a significant hazard, yet the sensitivity of wave heights to key source parameters remains poorly constrained. Using the non-hydrostatic multilayer HySEA model, we perform an extensive parametric study to assess the sensitivity of granular flow-generated tsunami wave heights at Stromboli volcano to six physical parameters: slide volume, initial submergence depth (elevation), density, basal friction, water-coupling coefficient, and source azimuth. A variance-based Sobol sensitivity analysis reveals that for the combined dataset of subaerial and submarine flows, the initial elevation (contributing &sim;61 % to output variance normalized to 100 %) and volume (&sim;22 %) are the dominant controls on maximum wave height. When analyzed separately, subaerial tsunamis are primarily controlled by volume (&sim;60 %), while submarine tsunamis show a balanced sensitivity to volume (&sim;35 %) and initial submergence depth (&sim;37 %). We identify distinct scaling relationships between maximum wave height and landslide volume: a linear one for submarine landslides, with an exponential decay in efficiency as a function of submergence depth; a logarithmic fit for subaerial landslides, where the efficiency of wave generation per unit volume decreases for larger events. These relationships, modulated by secondary parameters like friction, provide a quantitative framework for rapid tsunami hazard assessment. Our results demonstrate a crossover in hazard potential, where subaerial slides tend to produce larger tsunami waves for smaller volumes, while submarine slides can produce larger waves for larger volumes due to the absence of logarithmic saturation. These results constrain the scaling laws needed to quickly invert tsunami observations into source volumes (and viceversa) and improve probabilistic hazard assessments by identifying the parameters that dominate uncertainty at Stromboli and similar islands.