Large language models (LLMs) are increasingly used as collaborative partners in writing. However, this raises a critical challenge of authorship, as users and models jointly shape text across interaction turns. Understanding authorship in this context requires examining users’ evolving internal states during collaboration, particularly self-efficacy and trust. Yet, the dynamics of these states and their associations with users’ prompting strategies and authorship outcomes remain underexplored. We examined these dynamics through a study of 302 participants in LLM-assisted writing, capturing interaction logs and turn-by-turn self-efficacy and trust ratings. Our analysis showed that collaboration generally decreased users’ self-efficacy while increasing trust. Participants who lost self-efficacy were more likely to ask the LLM to edit their work directly, whereas those who recovered self-efficacy requested more review and feedback. Furthermore, participants with stable self-efficacy showed higher actual and perceived authorship of the final text. Based on these findings, we propose design implications for understanding and supporting authorship in human-LLM collaboration.