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We have performed 2D bulge/bar/disc decompositions using  g ,  r  and  i ‐band images of a representative sample of nearly 1000 galaxies from the Sloan Digital Sky Survey. We show that the Petrosian concentration index is a better proxy for the bulge‐to‐total ratio than the global Sérsic index. We show that pseudo‐bulges can be distinguished from classical bulges as outliers in the Kormendy relation. We provide the structural parameters and distributions of stellar masses of ellipticals, classical bulges, pseudo‐bulges, discs and bars, and find that 32 per cent of the total stellar mass in massive galaxies in the local universe is contained in ellipticals, 36 per cent in discs, 25 per cent in classical bulges, 3 per cent in pseudo‐bulges and 4 per cent in bars. Pseudo‐bulges are currently undergoing intense star formation activity and populate the blue cloud of the colour–magnitude diagram. Most (though not all) classical bulges are quiescent and populate the red sequence of the diagram. Classical bulges follow a correlation between the bulge Sérsic index and bulge‐to‐total ratio, while pseudo‐bulges do not. In addition, for a fixed bulge‐to‐total ratio, pseudo‐bulges are less concentrated than classical bulges. Pseudo‐bulges follow a mass–size relation similar to that followed by bars, and different from that followed by classical bulges. In the fundamental plane, pseudo‐bulges occupy the same locus as discs. While these results point out different formation processes for classical and pseudo‐bulges, we also find a significant overlap in their properties, indicating that the different processes might happen concomitantly. Finally, classical bulges and ellipticals follow offset mass–size relations, suggesting that high‐mass bulges might not be simply high‐mass ellipticals surrounded by discs.

Structural properties of pseudo‐bulges, classical bulges and elliptical galaxies: a Sloan Digital Sky Survey perspective