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How mass assembly occurs in galaxies and which process(es) contribute to thisactivity are among the most highly debated questions in galaxy formationtheories. This has motivated our survey MASSIV of 0.9<z<1.9 star-forminggalaxies selected from the purely flux-limited VVDS redshift survey. For thefirst time, we derive the relations between galaxy size, mass, and internalvelocity, and the baryonic Tully-Fisher relation, from a statisticallyrepresentative sample of star-forming galaxies. We find a dynamical mass thatagrees with those of rotating galaxies containing a gas fraction of ~20%,perfectly consistent with the content derived using the Kennicutt-Schmidtformulation and the expected evolution. Non-rotating galaxies have more compactsizes for their stellar component, and are less massive than rotators, but donot have statistically different sizes for their gas-component. We measure amarginal evolution in the size-stellar mass and size-velocity relations inwhich discs become evenly smaller with cosmic time at fixed stellar mass orvelocity, and are less massive at a given velocity than in the local Universe.The scatter in the Tully-Fisher relation is smaller when we introduce the S05index, which we interpret as evidence of an increase in the contribution togalactic kinematics of turbulent motions with cosmic time. We report apersistently large scatter for rotators in our relations, that we suggest isintrinsic, and possibly caused by complex physical mechanism(s) at work in ourstellar mass/luminosity regime and redshift range. Our results consistentlypoint towards a mild, net evolution of these relations, comparable to thosepredicted by cosmological simulations of disc formation for at least 8Gyr and adark halo strongly coupled with galactic spectrophotometric properties.

MASSIV: Mass Assembly Survey with SINFONI in VVDS. IV. Fundamental relations of star-forming galaxies at 1