Self-assembly is a process through which an organized structure can spontaneously form from simple parts. Taking inspiration from biological examples of self-assembly, we designed and built a water-based modular robotic system consisting of autonomous plastic tiles capable of aggregation on the surface of water. In this paper, we investigate the effect of the morphology (here: shape) of the tiles on the yield of the self-assembly process, that is, on the final amount of the desired aggregate. We describe experiments done with the real system as well as with a computer simulation thereof. We also present results of a mathematical analysis of the modular system based on chemical rate equations which point to a power-law relationship between yield rate and shape. Using the real system, we further demonstrate how through a single parameter (here: the externally applied electric potential) it is possible to control the self-assembly of propeller-like aggregates. Our results seem to provide a starting point (a) for quantifying the effect of morphology on the yield rates of self- assembly processes and (b) for assessing the level of modular autonomy and computational resources required for emergent functionality to arise.