In a sample of 5811 patents with US faculty as inventors, 26\% are assigned solely to firms rather than universities as dictated by US university employment policies and Bayh-Dole. We relate assignment to patent characteristics, university policy, and inventor field. Patents assigned to firms (whether established or start-ups with inventor as principal) are less basic than those assigned to universities suggesting firm assigned patents result from faculty consulting. Assignment to inventor-related start-ups is less likely the higher the share of revenue inventors receive from university-licensed patents. Firm assignment also varies by inventor field and whether the university is public or private.