We demonstrate that there are systematic scale errors in the [ Fe/H ] values determined by the Hamburg/ESO Survey ( and by the HK Survey by inference ) for certain extremely metal poor ( EMP ) highly C-enhanced giants . The consequences of these scale errors are that a ) the fraction of carbon stars at extremely low metallicities has been substantially overestimated in several papers in the recent literature b ) the number of EMP stars known is somewhat lower than has been quoted in the recent literature c ) the yield for EMP stars by the HK and the HES Survey is somewhat lower than is stated in the recent literature . A preliminary estimate for the frequency of Carbon stars among the giants in the HES sample with -4 < [ Fe/H ] < -2.0 dex is 7.4 \pm 2.9 % , and for C-rich giants with [ C/Fe ] \geq +1.0 dex is 14.4 \pm 4 % . We rely on the results of an extensive set of detailed abundance analyses of stars expected to have [ Fe/H ] \leq - 3.0 dex selected from the Hamburg/ESO Survey to establish these claims . These analyses of \sim 50 HES candidate extremely metal poor stars have been carried out in as homogeneous a manner as possible . Here we present the key results of detailed abundance analyses of 14 C-stars selected in this way About 80 % of such C-stars show highly enhanced Ba as well , with C enhanced by a factor of about 100 , and [ Ba/C ] roughly Solar . These stars often show prominent lead lines , and presumably are the remnants of the secondary in a mass transfer binary system where the former primary was an AGB star , which transferred substantial mass at that evolutionary stage . The remaining 20 % of the C-stars do not show an enhancemement of the s-process neutron capture elements around the Ba peak . They tend to be the most metal-poor stars studied . We suggest that they too result from mass transfer across a binary system . ( published abstract will be shorter due to space limitations )