The concentration of many transcription factors exhibit high cell-to-cell variability due to differences in synthesis, degradation, and cell size. How these factors are robust to fluctuations in concentration is poorly understood. Here we quantified the single cell levels of the YAP/TAZ transcriptional co-activators in parallel with cell morphology for over 400,000 single cells across 17 cell lines. We show the whole cell concentration of YAP/TAZ sub-scales with respect to size as cells grow during proliferation. However, the mean nuclear concentration of YAP/TAZ remains constant during the cell cycle. Theoretical modelling demonstrates that the extent to which whole cell YAP/TAZ dilutes in single cells during proliferative growth dictates the variability of YAP/TAZ levels across the population. Integrative analysis of imaging and proteomic data show the average nuclear YAP/TAZ concentration is predicted by differences in RAS/MAPK signalling, focal adhesion maturation, and nuclear transport processes. We developed a statistical framework capable of discriminating between perturbations that affect YAP/TAZ directly, or via changes in morphology. Deployment of these models on genetic screening data or small-molecule treatments reveal that inhibition of MEK, CDK4/6, LATS and RhoGTPases decouple nuclear YAP/TAZ from cell morphology by regulating nuclear translocation. Thus signalling activity couples size changes to YAP/TAZ translocation; leading to a stable pool of nuclear YAP/TAZ during proliferation. Significance Statement Many proteins dilute/concentrate with changes in cell size. It is unclear how robustness in cell signalling emerges across differently sized cells, with varying intracellular protein concentrations, over generations. Here, we have shown that despite whole cell dilution of the transcriptional co activators YAP/TAZ with increasing size, a steady-state nuclear concentration distribution is maintained across the population. Thus nuclear transport promotes robustness of signal response in the face of a dwindling cytoplasmic YAP/TAZ levels. An integrative approach revealed that focal adhesions, RAS/MAPK and nuclear import contributes to the the maintenance of YAP/TAZ nuclear levels. Cells appear to have evolved systems to ensure robustness against alterations to cell size during the cell cycle.