Although AI assistance can improve writing quality, it can also decrease feelings of ownership. Ownership in writing has important implications for attribution, rights, norms, and cognitive engagement, and designers of AI support systems may want to consider how system features may impact ownership. We investigate how the stage at which AI support for writing is provided (planning, drafting, or revising) changes ownership. In a study of short essay writing (between subjects, n = 253) we find that while any AI assistance decreased ownership, planning support only minimally decreased ownership, while drafting support saw the largest decrease. This variation maps onto the amount of text and ideas contributed by AI, where more text and ideas from AI decreased ownership. Notably, an AI-generated draft based on participants' own outline resulted in significantly more AI-contributed ideas than AI support for planning. At the same time, more AI contributions improved essay quality. We propose that writers, educators, and designers consider writing stage when introducing AI assistance.

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