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To tackle climate change, residential heating must become climate-neutral. Which technology cost-efficiently achieves this goal is a complex question, given the heterogeneity of buildings and existing infrastructure, as well as the uncertainty regarding future energy prices and infrastructure costs. The present article aims to disentangle this complexity by comparing the future costs of various decentralized and centralized climate-neutral heating options. Using Germany as a case study, we calculate the future levelized cost of ten heating technologies for different building and settlement types and a wide range of assumptions for uncertain parameters, including energy prices and grid fees. We find that electric heat pumps are most often the economical choice within the considered range of inputs. Decentralized heat pumps appear to be preferable in rural areas, while heating grids with central heat pumps seem equally attractive in more urban areas. Hydrogen boilers would be cost-efficient only in scenarios with low hydrogen prices and, even then, often limited to rural settlements. Heating with synthetic natural gas seems unlikely to be economical across a broad range of plausible assumptions. Our results allow us to draw conclusions for policymakers in the German context and offer insights for similar policy debates in other countries.