The simultaneous occurrence of extremely wet winters at multiple locations in the same region can contribute to widespread flooding and associated socio-economic losses. However, the change in the spatial extent of precipitation extremes is largely overlooked in climate change assessments. Employing new multi-thousand-year climate model simulations, we show that under both 2.0°C and 1.5°C warming scenarios, wintertime precipitation extreme extents would increase over about 80-90% of the Northern Hemisphere. Stabilising at 1.5°C rather than 2°C would reduce the average magnitude of the increase by 1.6-2 times. According to the climate model, the increased extents are caused by increases in precipitation intensity increasing rather than changes in the spatial organisation of the events. Relatively small percentage increases in precipitation intensities (e.g., by 4%) can drive disproportionately larger, by 1-2 orders of magnitude, growth in the spatial extents (by 97%).