Context : Weak G-band ( wGb ) stars are a very peculiar class of red giants ; they are almost devoided of carbon and often present mild lithium enrichment .
Despite their very puzzling abundance patterns , very few detailed spectroscopic studies existed up to a few years ago , which prevented any clear understanding of the wGb phenomenon .
We recently proposed the first consistent analysis of published data for a sample of 28 wGb stars and were able to identify them as descendants of early A-type to late B-type stars , although we were not able to conclude on their evolutionary status or the origin of their peculiar abundance pattern .

Aims : Using new high-resolution spectra , we present the study of a new sample of wGb stars with the aim of homogeneously deriving their fundamental parameters and surface abundances for a selected set of chemical species that we use to improve our insight on this peculiar class of objects .

Methods : We obtained high-resolution and high signal-to-noise spectra for 19 wGb stars in the southern and northern hemisphere that we used to perform consistent spectral synthesis to derive their fundamental parameters and metallicities , as well as the spectroscopic abundances for Li , C , ^ { 12 } C/ ^ { 13 } C , N , O , Na , Sr , and Ba .
We also computed dedicated stellar evolution models that we used to determine the masses and to investigate the evolutionary status and chemical history of the stars in our sample .

Results : We confirm that the wGb stars are stars with initial masses in the range 3.2 to 4.2 M _ { \odot } .
We suggest that a large fraction could be mildly evolved stars on the subgiant branch currently undergoing the first dredge-up , while a smaller number of stars are more probably in the core He burning phase at the clump .
After analysing their abundance pattern , we confirm their strong nitrogen enrichment anti-correlated with large carbon depletion , characteristic of material fully processed through the CNO cycle to an extent not known in evolved intermediate-mass stars in the field and in open clusters .
However , we demonstrate here that such a pattern is very unlikely owing to self-enrichment .

Conclusions : In the light of the current observational constraints , no solid self-consistent pollution scenario can be presented either , leaving the wGb puzzle largely unsolved .