Observations of diffuse starlight in the outskirts of galaxies are thought to be a fundamental source of constraints on the cosmological context of galaxy assembly in the $Lambda$CDM model. Such observations are not trivial because of the extreme faintness of such regions. In this work, we investigate the photometric properties of six massive early type galaxies (ETGs) in the VEGAS sample (NGC 1399, NGC 3923, NGC 4365, NGC 4472, NGC 5044, and NGC 5846) out to extremely low surface brightness levels, with the goal of characterizing the global structure of their light profiles for comparison to state-of-the-art galaxy formation models. We carry out deep and detailed photometric mapping of our ETG sample taking advantage of deep imaging with VST/OmegaCAM in the g and i bands. By fitting the light profiles, and comparing the results to simulations of elliptical galaxy assembly, we identify signatures of a transition between relaxed and unrelaxed accreted components and can constrain the balance between in situ and accreted stars. The very good agreement of our results with predictions from theoretical simulations demonstrates that the full VEGAS sample of $sim 100$ ETGs will allow us to use the distribution of diffuse light as a robust statistical probe of the hierarchical assembly of massive galaxies.