How organisms maintain cell size homeostasis is a long-standing problem that remains unresolved, especially in multicellular organisms. Recent experiments in diverse animal cell types demonstrate that within a cell population, cellular proliferation is low for small and large cells, but high at intermediate sizes. Here we use mathematical models to explore size-control strategies that drive such a non-monotonic profile resulting in the proliferation capacity being maximized at a target cell size. Our analysis reveals that most models of size control yield proliferation capacities that vary monotonically with cell size, and non-monotonicity requires two key mechanisms: (1) the growth rate decreases with increasing size for excessively large cells; and (2) cell division occurs as per the Adder model (division is triggered upon adding a fixed size from birth), or a Sizer-Adder combination. Consistent with theory, Jurkat T cell growth rates increase with size for small cells, but decrease with size for large cells. In summary, our models show that regulation of both growth and cell-division timing is necessary for size control in animal cells, and this joint mechanism leads to a target cell size where cellular proliferation capacity is maximized. Cell size control is a fundamental aspect of biology observed at different domains of life, but in most cases remains poorly understood 3-9. Two popular models for cell size control have been extensively studied and debated 10. In the "sizer" or the size-checkpoint model, cell-cycle transitions occur after attainment of a minimum cell mass or size, whereas in the "adder" model cells add a fixed amount of size in each division cycle independent of the daughter size. Strong evidence for adder has been reported in a diverse set of prokaryotes 11-21 and budding yeast 22. In cultured mammalian cell lines both adder, sizer and intermediate models can be observed 23,24 , while in the mouse epidermis in vivo, a sizer behavior is apparent 25. Recent experiments in animal cells revealed an intriguing observation about cellular proliferation that ties deeply into size control, suggesting an evolutionary reason why cells aim to maintain a certain size. In these experiments 1 , cells within a population were first sorted into several subpopulations based on cell size, and then the net proliferation (relative fold-change in cell count) was quantified for each cultured subpopulation after 72 h. Throughout the paper we refer to this relative increase in cell counts as the proliferation capacity. Interestingly, data across several cell types shows a non-monotonic bell-shaped profile, where the proliferation capacity is maximized at a target cell size (Fig. 1). Importantly, apoptosis rates were similar for large and average-sized cells, and hence the decrease in proliferation at higher sizes is not simply due to elevated cell death 1,26-30. Cellular proliferation measured via dye-dilution experiments showed identical trends for varying cells sizes (see supplementary figure S4 in 1), providing...