Self-sorting on surfaces is one of the big challenges that must be addressed in preparing the organic materials of the future. Here, we introduce a theoretical framework for templated self-sorting on surfaces, and validate it experimentally. In our approach, the transcription of two-dimensional information encoded in a monolayer on the surface into three-dimensional supramolecular architectures is quantified by the intrinsic templation efficiency, a thickness-independent value describing the fidelity of transcription per layer. The theoretical prediction that exceedingly high intrinsic efficiencies will be needed to experimentally observe templated self-sorting is then confirmed experimentally. Intrinsic templation efficiencies of up to 97%, achieved with a newly introduced templated synthesis strategy, result in maximal 47% effective templation efficiency at a thickness of 70 layers. The functional relevance of surface-templated self-sorting and meaningful dependences of templation efficiencies on structural modifications are demonstrated.