Abstract. Various observational estimates indicate growing mass loss at Antarctica's margins as well as heavier precipitation across the continent. Simulated future projections reveal that heavier precipitation, falling on Antarctica, may counteract amplified iceberg discharge and increased basal melting of floating ice shelves driven by a warming ocean. Here, we test how the ansatz (implementation in a mathematical framework) of the precipitation boundary condition shapes Antarctica's sea level contribution in an ensemble of ice sheet simulations. We test two precipitation conditions: we either apply the precipitation anomalies from CMIP5 models directly or scale the precipitation by the air temperature anomalies from the CMIP5 models. In the scaling approach, it is common to use a relative precipitation increment per degree warming as an invariant scaling constant. We use future climate projections from nine CMIP5 models, ranging from strong mitigation efforts to business-as-usual scenarios, to perform simulations from 1850 to 5000. We take advantage of individual climate projections by exploiting their full temporal and spatial structure. The CMIP5 projections beyond 2100 are prolonged with reiterated forcing that includes decadal variability; hence, our study may underestimate ice loss after 2100. In contrast to various former studies that apply an evolving temporal forcing that is spatially averaged across the entire Antarctic Ice Sheet, our simulations consider the spatial structure in the forcing stemming from various climate patterns. This fundamental difference reproduces regions of decreasing precipitation despite general warming. Regardless of the boundary and forcing conditions applied, our ensemble study suggests that some areas, such as the glaciers from the West Antarctic Ice Sheet draining into the Amundsen Sea, will lose ice in the future. In general, the simulated ice sheet thickness grows along the coast, where incoming storms deliver topographically controlled precipitation. In this region, the ice thickness differences are largest between the applied precipitation methods. On average, Antarctica shrinks for all future scenarios if the air temperature anomalies scale the precipitation. In contrast, Antarctica gains mass in our simulations if we apply the simulated precipitation anomalies directly. The analysis reveals that the mean scaling inferred from climate models is larger than the commonly used values deduced from ice cores; moreover, it varies spatially: the highest scaling is across the East Antarctic Ice Sheet, and the lowest scaling is around the Siple Coast, east of the Ross Ice Shelf. The discrepancies in response to both precipitation ansatzes illustrate the principal uncertainty in projections of Antarctica's sea level contribution.