Context. The evolution of galaxies is influenced by their local and global environment in the cosmic web. Galaxies with very old stellar populations (VO galaxies with D n (4000) index ≥ 1.75) mostly lie in the centres of galaxy clusters, where they evolve under the influence of processes characteristic of high-density cluster environments. However, VO galaxies have also been found in poor groups in global low-density environments between superclusters, which we call watershed regions. Aims. Our aim is to analyse the properties of galaxies in various cosmic environments with a focus on VO galaxies in the watershed regions to understand their evolution, and the origin of the large-scale morphology-density relation. Methods. We employ the Sloan Digital Sky Survey DR10 MAIN spectroscopic galaxy sample in the redshift range 0.009 ≤ z ≤ 0.200 to calculate the luminosity-density field of galaxies, to determine groups and filaments in the galaxy distribution, and to obtain data on galaxy properties. The luminosity-density field with smoothing length 8 h −1 Mpc, D8, characterises the global environment of galaxies. We analyse the group and galaxy contents of regions with various D8 thresholds. We divide groups into low-and highluminosity groups based on the highest luminosity of groups in the watershed region, L gr ≤ 15 × 10 12 h −2 L ⊙ . We compare the stellar masses, the concentration index, and the stellar velocity dispersions of quenched and star-forming galaxies among single galaxies, satellite galaxies, and the brightest group galaxies (BGGs) in various environments. Results. We show that the global density is most strongly related to the richness of galaxy groups. Its influence on the overall star formation quenching in galaxies is less strong. Correlations between the morphological properties of galaxies and the global density field are the weakest. The watershed regions with D8 < 1 are populated mostly by single galaxies, constituting 70 % of all galaxies there, and by low-luminosity groups. Still, approximately one-third of all galaxies in the watershed regions are VO galaxies. They have lower stellar masses, smaller stellar velocity dispersions, and stellar populations that are up to 2 Gyr younger than those of VO galaxies in other global environments. In higher density global environments (D8 > 1), the morphological properties of galaxies are very similar. Differences in galaxy properties are the largest between satellites and BGGs in groups. Conclusions. Our results suggest that galaxy evolution is determined by the birthplace of galaxies in the cosmic web, and mainly by internal processes which lead to the present-day properties of galaxies. This may explain the similarity of (VO) galaxies in extremely different environments.