In 2023, the European Union (EU) adopted the Regulation on Deforestation-free Products (EUDR) to curb deforestation and forest degradation linked to its agricultural and wood trade. While existing research has outlined how the regulation is expected to work when implemented from 2027, we still have a weak understanding of how these mechanisms are likely to play out across different country and commodity contexts. This study focuses on the conditions under which different outcomes emerge, encompassing both intended impacts and potential spillover effects. We highlight that the regulation is likely to produce heterogeneous, context-dependent outcomes in reducing future deforestation across commodities and countries, with EU market shares and associated deforestation embodied in EU trade being key conditions. Evaluated in absolute terms, the EUDR may not substantially reduce global deforestation or emissions, but it could be effective in certain contexts. Our results suggest that high EU market shares (e.g., cocoa, coffee) offer leverage, while low market shares (e.g., soy, palm oil) increase risks of market segregation and negative spillovers. The EUDR’s most significant source of leverage likely stems from its broader influence on forest and supply-chain governance among multinational companies and non-EU countries. Achieving this wider impact requires coordinated collaboration with both producer and other consumer countries.