We conduct a series of eight 45-day experiments with a global storm-resolving model (GSRM) to test the sensitivity of relative humidity R in the tropics to changes in model resolution and parameterizations. These changes include changes in horizontal and vertical grid spacing as well as in the parameterizations of microphysics and turbulence, and are chosen to capture currently existing differences among GSRMs. To link the R distribution in the tropical free troposphere with processes in the deep convective regions, we adopt a trajectory-based assessment of the last-saturation paradigm. The perturbations we apply to the model result in tropical mean R changes ranging from 0.5% to 8% (absolute) in the mid troposphere. The generated R spread is similar to that in a multi-model ensemble of GSRMs and smaller than the spread across conventional general circulation models, supporting that an explicit representation of deep convection reduces the uncertainty in tropical R. The largest R changes result from changes in parameterizations, suggesting that model physics represent a major source of humidity spread across GSRMs. The R in the moist tropical regions is disproportionately sensitive to vertical mixing processes within the tropics, which impact R through their effect on the last-saturation temperature rather than their effect on the evolution of the humidity since last-saturation. In our analysis the R of the dry tropical regions strongly depends on the exchange with the extra-tropics. The interaction between tropics and extratropics could change with warming and presage changes in the radiatively sensitive dry regions.