Nature of the white dwarfs and failed-AGB phenomenon as a function of initial stellar mass and Y_ini. The black thin line on the left delimits the (M; Y) domains where the stars become either He or CO white dwarfs; it crosses the white line that delimits the domains where helium ignition (when it occurs) starts with a flash or in non-degenerate conditions. The curved black thin line separates the stars that climb the AGB from those that do not (failed-AGB). Colors depict the age at the main sequence turn-off, with white dashed lines being isochrones with ages indicated in Gyr; the white area corresponds to the domain where stellar models predict main sequence lifetimes higher than 13.8 Gyr.