The third r-process peak (Os, Ir, Pt) is poorly understood due to observational challenges, with spectral lines located in the blue or near-ultraviolet region of stellar spectra. These challenges need to be overcome for a better understanding of the r-process in a broader context. To understand how the abundances of the third r-process peak are synthesised and evolve in the Universe, it is necessary to carry out a homogeneous chemical analysis of metal-poor stars using high-quality data observed in the blue region of the electromagnetic spectrum (< 400 nm). We provide a homogeneous set of abundances for the third r-process peak (Os, Ir, Pt) and Hf, increasing their availability in the literature by up to one order of magnitude. We performed a classical 1D, local thermodynamic equilibrium (LTE) analysis of four elements (Hf, Os, Ir, Pt) using ATLAS model atmospheres to fit synthetic spectra on high signal-to-noise-ratio spectra of 52 red giants observed with UVES/VLT in high resolution (> 40,000). Due to the heavy line blending involved, we carefully determined upper limits and uncertainties. The observational results are compared with state-of-the-art nucleosynthesis models. Our sample displays larger abundances of Ir (Z=77) in comparison to Os (Z=76), both of which have been measured in a few stars in the past. The results also suggest decoupling between the abundances of third r-process peak elements with respect to Eu (a rare earth element) in Eu-poor stars. This seems to contradict a co-production scenario of Eu and the third r-process peak elements Os, Ir, and Pt in the progenitors of these objects. Our results are challenging to explain from a nucleosynthetic point of view: the observationally derived abundances indicate the need for an additional early, primary formation channel (or a non-robust r-process).