The recent wave of generative AI (GAI) systems like Stable Diffusion that can produce images from human prompts raises controversial issues about creatorship, originality, creativity and copyright. This paper focuses on creatorship: who creates and should be credited with the outputs made with the help of GAI? Existing views on creatorship are mixed: some insist that GAI systems are mere tools, and human prompters are creators proper; others are more open to acknowledging more significant roles for GAI, but most conceive (...) of creatorship in an all-or-nothing fashion. We develop a novel view, called CCC (collective-centered creation), that improves on these existing positions. On CCC, GAI outputs are created by collectives in the first instance. Claims to creatorship come in degrees and depend on the nature and significance of individual contributions made by the various agents and entities involved, including users, GAI systems, developers, producers of training data and others. Importantly, CCC maintains that GAI systems can sometimes be part of a co-creating collective. We detail how CCC can advance existing debates and resolve controversies around creatorship involving GAI. (shrink)