This work presents a large consistent study of molybdenum (Mo) and ruthenium (Ru) abundances in the Milky Way. These two elements are important nucleosynthetic diagnostics. In our sample of 71 Galactic metal-poor field stars, we detect Ru and/or Mo in 51 of these (59 including upper limits). The sample consists of high-resolution, high signal-to-noise spectra covering both dwarfs and giants from [Fe/H]=-0.63 down to -3.16. Thus we provide information on the behaviour of Mo I and Ru I at higher and lower metallicity than is currently known. We find a wide spread in the Mo and Ru abundances, which is typical of heavy elements. This indicates that several formation processes, in addition to high entropy winds, can be responsible for the formation of Mo and Ru. The formation processes are traced by comparing Mo and Ru to elements (Sr, Zr, Pd, Ag, Ba, and Eu) with known formation processes. We find contributions from different formation channels, namely p-, slow (s-), and rapid (r-) neutron-capture processes. Molybdenum is a highly convolved element that receives contributions from several processes, whereas Ru is mainly formed by the weak r-process as is silver. We also compare our absolute elemental stellar abundances to relative isotopic abundances of presolar grains extracted from meteorites. Their isotopic abundances can be directly linked to the formation process (e.g. r-only isotopes) providing a unique comparison between observationally derived abundances and the nuclear formation process. The comparison to abundances in presolar grains shows that the r-/s-process ratios from the presolar grains match the total elemental chemical composition derived from metal-poor halo stars with [Fe/H]~ -1.5 to -1.1 dex. This indicates that both grains and stars around and above [Fe/H]=-1.5 are equally (well) mixed and therefore do not support a heterogeneous presolar nebula... Abridged.
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