Do the majority of stars form as gravitationally unbound?

Context. Some of the youngest stars (age less than or similar to 10 Myr) are clustered, while many others are observed scattered throughout star forming regions or in complete isolation. It has been intensively debated whether such scattered or isolated stars originate in star clusters or whether they form in truly isolated conditions. Exploring these scenarios could help set constraints on the conditions in which massive stars are formed. Aims. We adopted the assumption that all stars form in gravitationally bound star clusters embedded in molecular cloud cores (Gamma-1 model), which expel their natal gas early after their formation. Then we compared the proportion (fraction) of stars found in clusters with observational data. Methods. The star clusters are modelled by the code NBODY6, which includes binary stars, stellar and circumbinary evolution, gas expulsion, and the external gravitational field of their host galaxy. Results. We find that small changes in the assumptions in the current theoretical model estimating the fraction, Gamma, of stars forming in embedded clusters have a large influence on the results, and we present a counterexample as an illustration. This calls into question theoretical arguments about Gamma in embedded clusters and it suggests that there is no firm theoretical ground for low Gamma in galaxies with lower star formation rates (SFRs). Instead, the assumption that all stars form in embedded clusters is in agreement with observational data for the youngest stars (age less than or similar to 10 Myr). In the Gamma-1 scenario, the observed fraction of the youngest stars in clusters increases with the SFR only weakly; the increase is caused by the presence of more massive clusters in galaxies with higher SFRs, which release fewer stars to the field in proportion to their mass. The Gamma-1 model yields a higher fraction of stars in clusters for older stars (ages between 10 Myr and 300 Myr) than what is observed. This discrepancy can be caused by initially less compact clusters or a slightly lower star-formation efficiency than originally assumed in the Gamma-1 model, or by interactions of the post-gas-expulsion revirialised open clusters with molecular clouds.