Two currently debated problems in galaxy evolution, the fundamentally local or global nature of the main sequence of star formation and the evolution of the mass-size relation of star forming galaxies (SFGs), are shown to be intimately related to each other. As a preliminary step, a growth function 𝑔 is defined, which quantifies the differential change in half-mass radius per unit increase in stellar mass (𝑔 = 𝑑 log 𝑅 1/2 /𝑑 log 𝑀 ★ ) due to star formation. A general derivation shows that 𝑔 = 𝐾Δ(𝑠𝑆𝐹 𝑅)/𝑠𝑆𝐹 𝑅, meaning that 𝑔 is proportional to the relative difference in specific star formation rate between the outer and inner half of a galaxy, with 𝐾 a dimensionless structural factor for which handy expressions are provided. As an application, it is shown that galaxies obeying a fundamentally local main sequence also obey, to a good approximation, 𝑔 𝛾𝑛, where 𝛾 is the slope of the normalized local main sequence (𝑠𝑆𝐹 𝑅 ∝ Σ −𝛾 ★ ) and 𝑛 the Sersic index. An exact expression is also provided. Quantitatively, a fundamentally local main sequence is consistent with SFGs growing along a stationary mass-size relation, but inconsistent with the continuation at 𝑧 = 0 of evolutionary laws derived at higher 𝑧. This demonstrates that either the main sequence is not fundamentally local, or the mass-size relation of SFGs has converged to an equilibrium state some finite time in the past, or both.