Keeping a conversation going is the social glue of friendships. The DSM criteria for autism list difficulties with back-and-forth conversation but does not necessitate that all autistic children will be equally impacted. We carried out three studies (two pre-registered) with verbally fluent school children (age 5-9 years) to investigate how autistic and neurotypical children maintain a conversation topic. We also investigated within-group relationships between conversational ability and cognitive and sociocognitive predictors. Study 1 found autistic children were more likely than neurotypical controls to give off-topic and generic minimal responses (e.g. 'mm', 'oh') and were less likely to give non-verbal responses (e.g. nodding or use of facial affect to respond). Nonetheless, the autistic group provided topic-supporting responses 62% of the time, indicating some aspects of conversation topic maintenance are a relative strength. Studies 2 and 3 found large individual differences in topic-supporting conversational responding among both neurotypical and autistic children. These were positively related to theory of mind ability and age in both groups. Conversational skills lie on a continuum for the general population and differences by diagnostic group are a matter of degree. Given the importance for peer relationships, we suggest a whole classroom approach to supporting conversation skills in all children.