TETHER investigates how AI companions contribute to psychological dependencies in human-AI relationships by focusing on novel addiction pathways unique to AI interactions, such as anthropomorphism, emotional validation, and parasocial bond formation. Through four interconnected phases, the research explores foundational addiction mechanisms to establish a theoretical framework for understanding AI-specific dependencies. It analyzes the unique characteristics of AI companions — particularly their personalization capabilities and adaptive learning — that foster deeper engagement compared to traditional digital addictions. The study traces the transformation from casual engagement to psychological attachment, examining how factors like social isolation and individual vulnerabilities contribute to dependency formation. Finally, it investigates the escalation and retention mechanisms that maintain long-term engagement patterns, including self-reinforcing behavioral loops and compulsive usage. This comprehensive understanding will help address the emerging challenges of AI companion relationships while informing the development of safer and more responsible AI systems.