Look to Southeast Asia and especially Burma. The kings there took Asoka as their model and inscribed their temples with visual narratives and injunctions for the good, dharmatic life. On the king's perceived role as political and religious leader Thambiah's World Conqueror and World Renouncer will be useful for further information in this regard.
Dear Mr Gunasinghe, apart from Myanmar there are some inscriptions in Northern Thailand similar to those of Ashoka. They were made by the Buddhist ruler of Phayao in the XIV century. He even called himself tipitakadhara. There is some information here: Veidlinger D.M. Spreading the Dhamma. Honolulu, 2007.
Public inscriptions are early in the Ancient Near East, but are unknown in China until the First Emperor of Chin (ruled from 0221), who erected inscriptions at key points in his new empire. There is an excellent study of these, which I recommend: Martin Kern, The Stele Inscriptions of Ch'in Shih-huang (American Oriental Society 2000). Here again, as other responses point out, the Ashoka inscriptions may have provided a model; China was in touch with India from the beginning of the Buddhist period (05c).