The chemical abundances of elements such as barium and the lanthanides are essential to understand the nucleosynthesis of heavy elements in the early Universe as well as the contribution of different neutron capture processes (for example slow versus rapid) at different epochs. The Chemical Evolution of R-process Elements in Stars (CERES) project aims to provide a homogeneous analysis of a sample of metal-poor stars ( [Fe/H]<-1.5) to improve our understanding of the nucleosynthesis of neutron capture elements, in particular the r-process elements, in the early Galaxy. Our data consist of a sample of high resolution and high signal-to-noise ratio UVES spectra. The chemical abundances were derived through spectrum synthesis, using the same model atmospheres and stellar parameters as derived in the first paper of the CERES series. We measured chemical abundances or upper limits of seven heavy neutron capture elements (Ba, La, Ce, Pr, Nd, Sm, and Eu) for a sample of 52 metal-poor giant stars. We estimated through the mean shift clustering algorithm that at Ba/H =-2.4 and Fe/H =-2.4 a variation in the trend of X/Ba with X=La,Nd,Sm,Eu, versus Ba/H occurs. This result suggests that, for Ba/H $<$$-2.4$, Ba nucleosynthesis in the Milky Way halo is primarily due to the $r$-process, while for Ba/H <-2.4 the effect of the s-process contribution begins to be visible. In our sample, stars with Ba/Eu compatible with a Solar System pure r-process value (hereafter, r-pure) do not show any particular trend compared to other stars, suggesting r-pure stars may form in similar environments to stars with less pure r-process enrichments. Homogeneous investigations of high resolution and signal-to-noise ratio spectra are crucial for studying the heavy elements formation, as they provide abundances that can be used to test nucleosynthesis models as well as Galactic chemical evolution models.