Generative artificial intelligence models (GenAI) have attracted tremendous interest since the advent of ChatGPT, raising numerous opportunities and challenges. Yet their generative power has not yet been studied, leaving open the question of what is really generated by these tools. This paper proposes to address this question and characterize the various generative dimensions behind GenAI models. Thanks to the latest advancements in engineering design, that over the past decades have formalized the notion of generativity, we are able to characterize the various generative mechanisms at stake in GenAI. Besides a confirmation of GenAI tools’ generative power, we are able to reveal unexpected form of generativity, as such showing the limits of these tools but also drawing up some avenues for research.