Large language models (LLMs) often perform intermediate cognitive work while carrying out users' requests, yet it remains unclear which parts users intended to delegate and how they wanted to remain involved. This matters because consequential choices may go unnoticed, limiting users' ability to steer the process, while reviewing every step would make delegation burdensome. We examined this with 24 LLM users across three knowledge-work tasks, collecting 992 retrospective annotations of reasoning steps. From this, we developed taxonomies of LLM cognitive work, delegation enactment, and desired delegation protocols at the reasoning-step level. Our analysis revealed that participants viewed about half of all steps (48.6%) as AI-initiated, meaning the AI took on work they had not requested. Desired involvement varied with cognitive work and delegation enactment, even when contributions matched participants' intent. We propose design implications and sketches for supporting more deliberate cognitive delegation through flexible protocols and inspectable, revisable AI-initiated decisions.

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