Establishing relative role of internally and externally driven mechanisms responsible for disc and bulge growth is essential to understand the evolution of disc galaxies. In this context, we have studied the physical properties of disc galaxies without classical bulges in comparison to those with classical bulges since z similar to 0.9. Using images from the Hubble Space Telescope and Sloan Digital Sky Survey, we have computed both parametric and non-parametric measures, and examined the evolution in size, concentration, stellar mass, effective stellar mass density and asymmetry. We find that both disc galaxies with and without classical bulges have gained more than 50 per cent of their present stellar mass over the last similar to 8 Gyr. Also, the increase in disc size is found to be peripheral. While the average total (Petrosian) radius almost doubles from z similar to 0.9 to z similar to 0, the average effective radius undergoes a marginal increase in comparison. Additionally, increase in the density of the inner region is evident through the evolution of both concentration and effective stellar mass density. We find that the asymmetry index falls from higher to lower redshifts, but this is more pronounced for the bulgeless disc sample. Also, asymmetry correlates with the global effective radius, and concentration correlates with the global Sersic index, but better so for higher redshifts only. The substantial increase in mass and size indicates that accretion of external material has been a dominant mode of galaxy growth, where the circumgalactic environment plays a significant role.