We provide an individual analysis of 94 carbon enhanced metal-poor stars showing an s-process enrichment (CEMP-s) collected from the literature. The s-process enhancement observed in these stars is ascribed to mass transfer by stellar winds in a binary system from a more massive companion evolving faster toward the asymptotic giant branch (AGB) phase. The theoretical AGB nucleosynthesis models have been presented in Paper I. Several CEMP-s stars show an enhancement in both s and r-process elements (CEMP-s/r). In order to explain the peculiar abundances observed in CEMP-s/r stars, we assume that the molecular cloud from which CEMP-s formed was previously enriched in r-elements by Supernovae pollution. A general discussion and the method adopted in order to interpret the observations have been provided in Paper II. We present in this paper a detailed study of spectroscopic observations of individual stars. We consider all elements from carbon to bismuth, with particular attention to the three s-process peaks, ls (Y, Zr), hs (La, Nd, Sm) and Pb, and their ratios [hs/ls] and [Pb/hs]. The presence of an initial r-process contribution may be typically evaluated by the [La/Eu] ratio. We found possible agreements between theoretical predictions and spectroscopic data. In general, the observed [Na/Fe] (and [Mg/Fe]) provide information on the AGB initial mass, while [hs/ls] and [Pb/hs] are mainly indicators of the s-process efficiency. A range of 13C-pocket strengths is required to interpret the observations. However, major discrepancies between models and observations exist. We highlight star by star the agreements and the main problems encountered and, when possible, we suggest potential indications for further studies. These discrepancies provide starting points of debate for unsolved problems ...
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