Abstract: We will look at several models of cluster growths on fractal graphs and investigate the scaling limits. The models we investigate are: internal DLA, in which particles perform random walks until reaching unoccupied sites; Abelian and divisible sandpiles in which each site distributes its excess mass equally among its neighbors; and rotor aggregation which is a deterministic counterpart of internal DLA. We will review some results that confirm that these models have the same limit shape, and finally we look at them on spaces with fractal properties such as the Sierpinski gasket. We let the spacing in the gasket go to zero, consider the models on the rescaled spaces, and we prove that the models have a scaling limit that can be described as the solution of an obstacle problem in R². This is based on recent work (2022) with Uta Freiberg, Nico Heizmann and Robin Kaiser.