Context: .Satellite accretion events have been invoked for mimicking the internal secular evolutionary processes of bulge growth. However, N-body simulations of satellite accretions have paid little attention to the evolution of bulge photometric parameters, to the processes driving this evolution, and to the consistency of this evolution with observations. Aims: .We want to investigate whether satellite accretions indeed drive the growth of bulges, and whether they are consistent with global scaling relations of bulges and discs. Methods: .We perform N-body models of the accretion of satellites onto disc galaxies. A Tully-Fisher (M∝ V_rotα_TF}) scaling between primary and satellite ensures that density ratios, critical to the outcome of the accretion, are realistic. We carry out a full structural, kinematic and dynamical analysis of the evolution of the bulge mass, bulge central concentration, and bulge-to-disc scaling relations. Results: . The remnants of the accretion have bulge-disc structure. Both the bulge-to-disc ratio (B/D) and the Sérsic index (n) of the remnant bulge increase as a result of the accretion, with moderate final bulge Sérsic indices: n = 1.0 to 1.9. Bulge growth occurs no matter the fate of the secondary, which fully disrupts for α_TF=3 and partially survives to the remnant center for α_TF = 3.5 or 4. Global structural parameters evolve following trends similar to observations. We show that the dominant mechanism for bulge growth is the inward flow of material from the disc to the bulge region during the satellite decay. Conclusions: .The models confirm that the growth of the bulge out of disc material, a central ingredient of secular evolution models, may be triggered externally through satellite accretion.