ABSTRACT We study the rest-frame optical mass–size relation of bulges and discs from z ∼ 2 to z ∼ 0 for a complete sample of massive galaxies in the CANDELS fields using two-component Sérsic models. Discs and star-forming galaxies follow similar mass–size relations. The mass–size relation of bulges is less steep than the one of quiescent galaxies (best-fitting slope of 0.7 for quiescent galaxies against 0.4 for bulges). We find little dependence of the structural properties of massive bulges and discs with the global morphology of galaxies (disc versus bulge dominated) and the star formation activity (star-forming versus quiescent). This result suggests similar bulge formation mechanisms for most massive galaxies and also that the formation of the bulge component does not significantly affect the disc structure. Our results pose a challenge to current cosmological models that predict distinct structural properties for stellar bulges arising from mergers and disc instabilities.