In this study, we have carried out a detailed, statistical analysis of isolated model galaxies, taking advantage of publicly available hierarchical galaxy formation models. To select isolated galaxies, we employ 2D methods widely used in the observational literature, as well as a more stringent 3D isolation criterion that uses the full 3D-real space information. In qualitative agreement with observational results, isolated model galaxies have larger fractions of late-type, star forming galaxies with respect to randomly selected samples of galaxies with the same mass distribution. We also find that the samples of isolated model galaxies typically contain a fraction of less than 15 per cent of satellite galaxies, that reside at the outskirts of their parent haloes where the galaxy number density is low. Projection effects cause a contamination of 2D samples of about 18 per cent, while we estimate a typical completeness of 65 per cent. Our model isolated samples also include a very small (few per cent) fraction of bulge dominated galaxies (B/T > 0.8) whose bulges have been built mainly by minor mergers. Our study demonstrates that about 65-70 per cent of 2D isolated galaxies that are classified as isolated at z = 0 have indeed been completely isolated since z = 1 and only 7 per cent have had more than 3 neighbours within a comoving radius of 1 Mpc. Irrespectively of the isolation criteria, roughly 45 per cent of isolated galaxies have experienced at least one merger event in the past (most of the mergers are minor, with mass ratios between 1:4 and 1:10). The latter point validates the approximation that isolated galaxies have been mainly influenced by internal processes.
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