Universities have traditionally developed training and research functions. In the last decades they have adopted a third function: interaction with industry. Several instruments have been employed: R&D contracts, technological support, consultancy and others like patenting, on which technology leading country universities have placed a special emphasis for some years. Although it has been a matter of concern, the incipient literature on the topic has not created a specific model of the factors affecting the generation of university patents. In this work, departing from the recognition that a relation between them and the amount of R&D carried out by university departments exist, the fitness of a knowledge production function has been tested with university patents as an output. The application made on the available data of the Polytechnic University of Valencia shows that count data models are appropriate to represent the mentioned relationship. The results demonstrate that current R&D exerts a greater influence on patents than past R&D, that science-dependent fields of knowledge present higher technological opportunities and that larger departments tend to apply for a relatively lower number of patents. On the other hand, the decomposition of R&D by source of funding allows us to observe that publicly funded research is the most important source for the generation of patents, but that synergy exists with complementary funding by industry. The decomposition of R&D by type of activity indicates, in turn, that the activities of knowledge transfer proper do not head to the application for patents. It may be concluded that the rise of university patents does not represent a move out of fundamental research, but also that they do not necessarily contribute to technology transfer and progress. Some lessons for catching-up countries arise.