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Hybrid rocket motors with paraffin-based fuels are of interest due to higher regression rates compared to other polymers. During paraffin combustion, a liquid layer forms on the fuel surface that, together with shearing forces from the oxidizer flow, results in the formation of instabilities at the fuel-oxidizer interface. These instabilities lead to the formation and entrainment of heterogeneous sized liquid droplets into the main flow and the combusting droplets result in higher motor output. The atomization process begins with droplet formation and ends with droplet pinch-off. The goal of this paper is to conduct an uncertainty quantification (UQ) analysis of the pinch-off process characterized by a pinch-off volume ($$V_{po}$$) and time ($$t_{po}$$). We study these quantities of interest (QoIs) in the context of a slab burner setup. We have developed a computationally expensive mathematical model that describes droplet formation under external forcing and trained an inexpensive Gaussian Process surrogate of the model to facilitate UQ. We use the pinch-off surrogate to forward propagate uncertainty of the model inputs to the QoIs and conduct two studies: one with gravity present and one without gravity effects. After forward-propagating the uncertainty of the inputs using the surrogate, we concluded that both QoIs have right-skewed distributions, corresponding to larger probability densities towards smaller pinch-off volumes and times. Specifically, for the pinch-off times, the resulting distributions reflect the effect of gravity acting against droplet formation, resulting in longer pinch-off times compared to the case where there is no gravity.