The earliest compositional differentiation of the terrestrial planets, the formation of their outgassed atmospheres, and the existence of condensed water oceans over their solid mantles, are conditioned by magma ocean (MO) formation and solidification. Recent studies have suggested that depending on the planet initial water content and its orbital distance to the sun, two types of conditions, with (I) or without (II) water ocean, can prevail at the end of the MO phase. We use a coupled interior-atmosphere model of MO thermal evolution to go further and study systematically the influence of the planet initial CO2 content on the resulting surface conditions (temperature, volatiles, condensed water) at the end of the MO phase. The position of the boundary between the two regimes is shown to depend also on the initial CO2 content.