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The decarbonization of electricity systems calls for transparent methods to quantify how carbon emissions propagate through increasingly complex and decentralized grids, particularly as distribution grids evolve into prosumer-dominated systems with high penetration of distributed energy resources. This work presents a framework for carbon flow tracing in distribution grids, enabling the attribution of carbon intensities to end users and prosumers based on physical power flows. Three tracing approaches are developed and compared: a lossless method (LL), a lossless method with prosumer priority (LL-P), and a losses allocation method (LA) that explicitly accounts for network losses. The framework is applied using both a small toy example and a synthetic distribution grid in Dietlikon, Switzerland. Results reveal significant temporal and spatial variations in attributed emission intensities, especially during periods of high photovoltaic generation. The proposed framework can support network planning, operational analysis, carbon monitoring, and distributed energy resource deployment within the context of the energy transition.