In the past decades migration has been the dominant explanation employed by scholars to explain how the Kharosthi script and other innovations from North-West India spread to the Tarim Basin region during the first centuries CE. This article is a case study which seeks to challenge this migration scenario, based on a close study of the textual and material evidence available from the Krorainian Kingdom which occupied parts of the Southern Tarim Basin in antiquity. First evidence which challenges the migration scenario is presented, looking both at linguistic and literary evidence, as well as evidence for continuity in local practice and belief. An alternative scenario based on exchange and interaction is proposed towards the end of the article, arguing that to suppose large scale migration is unnecessary to explain the phenomenon at hand. For this alternative the article draw upon ideas from recent archaeological studies on the pre-historic Central Eurasia.