The emergence of generative artificial intelligence and increasingly agentic technologies, fundamentally alters the relationship between humans and machines. Yet, we lack a nuanced understanding of what human-machine relationships entail and how they function collaboratively. In this study, we leverage a tripartite typology, ranging from task substitution to task augmentation to task assemblage, to examine human-machine relationships as bundles of evolving relations rather than stable entities. Using a case survey of multiple case studies, we identified three relational attributes entailing human-machine relationships—technological embodiment, relational configuration, and relational functioning. Our most significant contribution is the development of a framework that juxtaposes the tripartite typology on a horizontal axis and relational attributes on a vertical axis, generating a three-by-three matrix of nine relational attributes’ dimensions. The framework contributes to theory on human-machine relationships. First, we provide substantiation to conceptually distinguish between different types of human-machine relationships, facilitating the recognition of observed and novel human-AI hybrids and their consequences. Second, we provide support for a shift toward a relational perspective of human-machine relationships, focusing on the attributes of dynamic relations that can flexibly respond to emergent situations such as human-LLM collaboration. Third, we provide theoretical evidence for a hierarchy of increasing relational complexity from task substitution to task augmentation to task assemblage. Our findings provide a novel way to orient researchers toward particular questions and phenomena that leverage human-machine relationships to improve how organizations operate.