Many recent news reports have claimed that content generated by large language models (LLMs) is taking over the web. However, these claims are typically not based on a representative sample of the web and the methodology underlying them is often opaque. Moreover, when aiming to minimize the chances of falsely attributing human-authored content to LLMs, we find that detectors of LLM-generated text perform much worse than advertised. Consequently, we lack an understanding of the true prevalence and characteristics of LLM content on the web. We describe DeGenTWeb which systematically identifies LLM-dominant websites: sites whose content has been generated using LLMs with little human input. We show how to adapt detectors of LLM-generated text for use on web pages, and how to aggregate detection results from multiple pages on a site for accurate site-level categorization. Using DeGenTWeb, we find that LLM-dominant sites are highly prevalent both in data from Common Crawl and in Bing's search results, and that this share is growing over time. We also show that continuing to accurately identify such sites appears challenging given the capabilities of the latest LLMs.