We present a detailed surface density analysis of a large sample of simulated collisionless mergers of disc galaxies with bulges (mass ratios 1:1, 2:1, 3:1, 4:1 and 6:1) and without bulges (mass ratios 1:1 and 3:1). A dissipative component was not included. The randomly projected remnants were fit with a single Sérsic function and a Sérsic function plus an exponential. They were classified, according to their bulge-to-total (B/T) ratio, either as a one-component system or as a two-component system. In general, projection effects change the classification of a remnant. Only merger remnants of discs with bulges show properties similar to observed early-type galaxies. Their B/T ratios are in the range 0.2 < B/T < 1. Surprisingly, the initial mass ratio has a weak influence on the distributions of B/T, effective radius and Sérsic index n. For all one-component projections (~60 per cent of all projections), the Sérsic index distribution peaks at 3 < n < 4. However, the mass ratio is tightly linked to the properties of the outer exponential components which resemble pressure-supported, spheroidal haloes for 1:1 and 2:1 remnants and elongated heated discs for 6:1 remnants. We found distinct correlations between the fitting parameters which are very similar to observed relations (e.g. larger bulges have lower effective surface densities). No indications for a correlation between the surface density profiles and other global parameters like remnant masses, isophotal shapes or central velocity dispersions are found. The remnants have properties similar to giant elliptical galaxies in the intermediate-mass regime. A binary disc merger origin for all early-type galaxies, especially the most massive ones, is unlikely. Observed nearby merger remnants have properties similar to the simulated remnants. They can have formed from binary disc mergers and might evolve into early-type galaxies within a few Gyr.