Tropical forests are highly diverse ecosystems, but within such forests there can be large patches dominated by a single tree species. The myriad presumed mechanisms that lead to the emergence of such monodominant areas is currently the subject of intensive research. We used the most generic of these mechanisms, large seed mass and low dispersal ability of the monodominant species, in a spatially explicit model. The model represents seven identical species with long-distance dispersal of small seeds, competing with one potentially monodominant species with short-distance dispersal of large seeds. Monodominant patches emerged and persisted only for a narrow range of species traits; these results have the characteristic features of phase transitions. Additional mechanisms may explain monodominance in different ecological contexts, but our results suggest that percolation-like phenomena and phase transitions might be pervasive in this type of system.