Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the r-process. We predict r-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determine for the first time systematic uncertainty bands -related to mass modelling -for r-process abundances in realistic astrophysical scenarios. We find that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: abundance peaks and troughs are reflected in trends of neutron separation energy. Further advances in nuclear theory and experiments, when linked to observations, will help in the understanding of astrophysical conditions in extreme r-process sites. Introduction -Understanding the origin of elements in nature is one of the outstanding questions in science. Here, the synthesis of the heavy elements represents a difficult interdisciplinary challenge. Half of the heavy elements up to bismuth and all of the thorium and uranium in the Universe are produced by the rapid capture of neutrons in the r-process [1]. This process requires high neutron densities and involves extreme neutron-rich nuclei not yet produced in the laboratory.In recent years, much progress has been made toward this problem in both astrophysics and nuclear physics. In astrophysics, multidimensional hydrodynamic simulations including improved microphysics indicate that (i) neutrino-driven winds following core-collapse supernovae are not neutron-rich enough to produce heavy elements as suggested in [2] (see Ref.[3] for a review); (ii) a rare kind of core-collapse supernova triggered by magnetic fields leads to neutron-rich jets where the r-process can occur [4][5][6]; and (iii) neutron star mergers (as suggested in [7] and preliminarily studied in [8]) -are excellent candidates for the synthesis of heavy elements [9][10][11] even if their contribution to the early galaxy is still under discussion. Some studies show that neutron star mergers provide an important contribution to the solar system rprocess, but this is not enough to explain the abundances in the oldest observed stars, see e.g., [12][13][14]. In contrast, other models can explain the r-process abundances at all metallicities solely based on the neutron star merger scenario [15].Experimentally, there has been impressive progress in approaching r-process nuclei, see [16][17][18][19][20][21] and references quoted therein. New-generation radioactive ion beam facilities [22][23][24] will be able to reach a range of nuclei