We use the same physical model to simulate four galaxies that match the relation between stellar and total mass, over a mass range that includes the vast majority of disc galaxies. The resultant galaxies, part of the Making Galaxies in a Cosmological Context (MaGICC) programme, also match observed relations between luminosity, rotation velocity, size, colour, star formation rate, H i mass, baryonic mass and metallicity. Radiation energy feedback from massive stars and supernova energy balance the complex interplay between cooling gas, regulated star formation, large-scale outflows and recycling of gas in a manner which correctly scales with the mass of the galaxy. Outflows, driven by the expansion of shells and superbubbles of overlapping supernova explosions, also play a key role in simulating galaxies with exponential surface brightness profiles, flat rotation curves and dark matter cores. Our study implies that large-scale outflows are the primary driver of the dependence of disc galaxy properties on mass. We show that the degree of outflows invoked in our model is required to meet the constraints provided by observations of O vi absorption lines in the circumgalactic media of nearby galaxies.