The last decade has seen widespread adoption of Machine Learning (ML) components in software systems. This has occurred in nearly every domain, from natural language processing to computer vision. These ML components range from relatively simple neural networks to complex and resource-intensive large language models. However, despite this widespread adoption, little is known about the supply chain relationships that produce these models, which can have implications for compliance and security. In this work, we conducted an extensive analysis of 760,460 models and 175,000 datasets extracted from the popular model-sharing site Hugging Face. First, we evaluate the current state of documentation in the Hugging Face supply chain, report real-world examples of shortcomings, and offer actionable suggestions for improvement. Next, we analyze the underlying structure of the existing supply chain. Finally, we explore the current licensing landscape against what was reported in previous work and discuss the unique challenges posed in this domain. Our results motivate multiple research avenues, including the need for better license management for ML models/datasets, better support for model documentation, and automated inconsistency checking and validation. We make our research infrastructure and dataset available to facilitate future research.