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We present half-light sizes measured from H${\alpha}$ emission tracingstar-formation in 281 star-forming galaxies from the KMOS3D survey at 0.7 < z <2.7. Sizes are derived by fitting 2D exponential disk models, with bootstraperrors averaging 20%. H${\alpha}$ sizes are a median (mean) of 1.19 (1.26)times larger than those of the stellar continuum, which due to radial dustgradients places an upper limit on the growth in stellar size via starformation, with just 43% intrinsic scatter. At fixed continuum size theH${\alpha}$ size shows no residual trend with stellar mass, star formationrate, redshift or morphology. The only significant residual trend is with theexcess obscuration of H${\alpha}$ by dust, at fixed continuum obscuration. Thescatter in continuum size at fixed stellar mass is likely driven by the scatterin halo spin parameters. The stability of the ratio of H${\alpha}$ size tocontinuum size demonstrates a high degree of stability in halo spin and in thetransfer of angular momentum to the disk over a wide range of physicalconditions and cosmic time. This may require local regulation by feedbackprocesses. The implication of our results, as we demonstrate using a toy model,is that our upper limit on star-formation driven growth is sufficient only toevolve star-forming galaxies approximately along the observed size-massrelation, consistent with the size growth of galaxies at constant cumulativeco-moving number density. To explain the observed evolution of the size-massrelation of star-forming disk galaxies other processes, such as thepreferential quenching of compact galaxies or galaxy mergers, may be required.

The regulation of galaxy growth along the size-mass relation by star-formation, as traced by H${\alpha}$ in KMOS$^{3D}$ galaxies at 0.7 < z < 2.7