Maintenance of cellular size is a fundamental systems level process that requires balancing of cell growth with proliferation. This is achieved via the cell division cycle, which is driven by the sequential accumulation and destruction of cyclins. The regulatory network around these cyclins, particularly in G1, has been interpreted as a size control network in budding yeast, and cell size as being decisive for the START transition. However, it is not clear why disruptions in the G1 network may lead to altered size rather than loss of size control, or why the S-G2-M duration also depends on nutrients. With a mathematical population model comprised of individually growing cells, we show that cyclin translation would suffice to explain the observed growth rate dependence of cell volume at START. Moreover, we assess the impact of the observed bud-localisation of the G2 cyclin CLB2 mRNA, and find that localised cyclin translation could provide an efficient mechanism for measuring the biosynthetic capacity in specific compartments: The mother in G1, and the growing bud in G2. Hence, iteration of the same principle can ensure that the mother cell is strong enough to grow a bud, and that the bud is strong enough for independent life. Cell sizes emerge in the model, which predicts that a single CDK-cyclin pair per growth phase suffices for size control in budding yeast, despite the necessity of the cell cycle network around the cyclins to integrate other cues. Size control seems to be exerted twice, where the G2/M control affects bud size through bud-localized translation of CLB2 mRNA, explaining the dependence of the S-G2-M duration on nutrients. Taken together, our findings suggest that cell size is an emergent rather than a regulatory property of the network linking growth and proliferation.