We have carried out a detailed abundance analysis using high dispersion spectra from HIRES at Keck for a sample of 16 carbon stars found among candidate extremely metal-poor ( EMP ) stars from the Hamburg/ESO Survey . We find that the Fe-metallicities for the cooler C-stars ( T _ { eff } \sim 5100 K ) have been underestimated by a factor of \sim 10 by the standard HES survey tools . The results presented here provided crucial supporting data used by ( 39 ) to derive the frequency of C-stars among EMP stars . C-enhancement in these EMP C-stars appears to be independent of Fe-metallicity and approximately constant at \sim 1/5 the solar \epsilon ( C ) . The C-enhancement shows some evidence of decreasing with decreasing T _ { eff } ( increasing luminosity ) , presumably due to mixing and dredge-up of C-depleted material . The mostly low ^ { 12 } C/ ^ { 13 } C ratios ( \sim 4 ) and the high N abundances in many of these stars suggest that material which has been through proton burning via the CN cycle comprises most of the stellar envelope . C-enhancement in this sample is associated with strong enrichment of heavy nuclei beyond the Fe-peak for 12 of the 16 stars . The remaining C-stars from the HES , which tend to be the most Fe-metal poor , show no evidence for enhancement of the heavy elements . Very high enhancements of lead are detected in some of the C-stars with highly enhanced Ba . The strong lead lines , the high Ba/Eu ratios , and the high ratios of abundances of the diagnostic elements in the first and second s -process peak demonstrate that the s -process is responsible for the enhancement of the heavy elements for the majority of the C-stars in our sample . The low ^ { 12 } C/ ^ { 13 } C ratios and large C and N enhancements of the EMP C-stars are more extreme than those of intrinsic AGB C-stars of near solar Fe-metallicity , but closer to the composition of CH stars . Our subsample of EMP C-stars without s -process enhancement is reminiscent of the R-type C-stars in the solar neighborhood ; thus we expect that they are formed by similar mechanisms . We suggest that both the s -process rich and Ba-normal C-stars result from phenomena associated with mass transfer in binary systems . This leads directly to the progression from C-stars to CH stars and then to Ba stars as the Fe-metallicity increases .