We present kinetic Monte Carlo simulations of submonolayer epitaxial growth with a mobile intermediate polyatomic cluster, inspired by the observations of graphene epitaxy on Ru(0001) and lr(111). We suppose that deposited atoms diffuse on the surface and collide to form tetra mers, which also diffuse on the surface. Immobile islands are formed when j tetramers collide. We study the temperature dependence of all surface species as a function of j. Unlike all other growth scenarios, the adatom density at the onset of nucleation increases with temperature for large enough j. Other characteristics, such as the island-size distribution and the temperature dependence of the island density, also show qualitatively different behavior from growth based on adatom kinetics.