Size distributions and other geometric properties of mesoscale convective systems (MCSs), identified as clusters of adjacent pixels exceeding a precipitation threshold in satellite radar images, are examined with respect to a recently identified critical range of water vapor. Satellite microwave estimates of column water vapor and precipitation show that the onset of convection and precipitation in the tropics can be described as a phase transition, where the rain rate and likelihood of rainfall suddenly increase as a function of water vapor. This is confirmed in Tropical Rainfall Measuring Mission radar data used here. Percolation theory suggests that cluster properties should be highly sensitive to changes in the density of occupied pixels, which here translates into a rainfall probability, which in turn sensitively depends on the water vapor. To confirm this, clusters are categorized by their prevalent water vapor. As expected, mean cluster size and radius of gyration strongly increase as the critical water vapor is approached from below. In the critical region one finds scale-free size distributions spanning several orders of magnitude. Large clusters are typically from the critical region: at low water vapor most clusters are small, and supercritical water vapor values are too rare to contribute much. The perimeter of the clusters confirms previous observations in satellite, field, and model data of robust nontrivial scaling. The well-known area-perimeter scaling is fully compatible with the quantitative prediction from the plausible null model of gradient percolation, where the accessible hull is a fractal object with dimension 4/3.