Generative AI (GenAI) is increasingly used in collaborative learning, yet its effects on how groups regulate collaboration remain unclear. Effective collaboration depends not only on what groups discuss, but on how they jointly manage goals, participation, strategy use, monitoring, and repair through co-regulation and socially shared regulation. We compared collaborative regulation between Human-AI and Human-Human groups in a parallel-group randomised experiment with 71 university students completing the same collaborative tasks with GenAI either available or unavailable. Focusing on human discourse, we used statistical analyses to examine differences in the distribution of collaborative regulation across regulatory modes, regulatory processes, and participatory focuses. Results showed that GenAI availability shifted regulation away from predominantly socially shared forms towards more hybrid co-regulatory forms, with selective increases in directive, obstacle-oriented, and affective regulatory processes. Participatory-focus distributions, however, were broadly similar across conditions. These findings suggest that GenAI reshapes the distribution of regulatory responsibility in collaboration and offer implications for the human-centred design of AI-supported collaborative learning.