core at the tip of the red giant branch(RGB). The electron degeneracy of the surrounding material leads to a runaway of the He burning, the He core flash. The quoted authors discovered that the small entropy barrier between hydrogen- and helium-rich material in Pop. III stars allows the convective zone, which is produced by the huge energy release of He burning, to penetrate the overlying hydrogen-rich layers. The resulting inward migration of protons into high-temperature regions (referred to as , hereinafter HEFM) leads to a H shell flash. As a consequence, when the convective envelope is deepening and merging with the H-flash driven convective zone (HCZ) later on, the surface is enriched with a large amount of matter that has experienced He-burning reactions and furthermore has been processed in H fusion during the H-flash. Thus, the chemical composition of the initially metal-free stellar surface is strongly altered and in particular carbon-enriched. These results provide an attractive working hypothesis for explaining the peculiar chemical patterns observed in extremely metal-deficient stars.

In a previous paper [@WCSS00 hereinafter Paper I], we have investigated the evolutionary properties of low-mass metal-free objects from the Zero Age Main Sequence (ZAMS) to the He-flash at the tip 