This paper studies the ongoing diffusion of renminbi (RMB) trading across the globe, the first of such research of an international currency. It analyses the distribution in offshore RMB trading in 2013 and 2016 using comprehensive data from the Triennial Central Bank Survey of foreign exchange markets. In 2013, Asian centers favored by the policy of RMB internationalization had disproportionate shares in global RMB trading. Over the following three years, RMB trading seemed to converge to the spatial pattern of all currencies, with a half-life of seven to eight years. The previously most traded emerging market currency, the Mexican peso, shows a similar pattern, although it is converging to the global norm more slowly. Three other emerging market currencies show a qualitatively similar evolution in the geography of their offshore trading. Overall, the RMB's internationalization is tracing an arc from the influence of administrative measures to the working of market forces.