In this paper we present the first comprehensive bibliometric analysis of eleven open-access mega-journals (OAMJs). OAMJs are a relatively recent phenomenon, and have been characterised as having four key characteristics: large size; broad disciplinary scope; a Gold-OA business model; and a peer-review policy that seeks to determine only the scientific soundness of the research rather than evaluate the novelty or significance of the work. Our investigation focuses on four key modes of analysis: journal outputs (the number of articles published and changes in output over time); OAMJ author characteristics (nationalities and institutional affiliations); subject areas (the disciplinary scope of OAMJs, and variations in sub-disciplinary output); and citation profiles (the citation distributions of each OAMJ, and the impact of citing journals). We found that while the total output of the eleven mega-journals grew by 14.9% between 2014 and 2015, this growth is largely attributable to the increased output of Scientific Reports and Medicine. We also found substantial variation in the geographical distribution of authors. Several journals have a relatively high proportion of Chinese authors, and we suggest this may be linked to these journals' high Journal Impact Factors (JIFs). The mega-journals were also found to vary in subject scope, with several journals publishing disproportionately high numbers of articles in certain sub-disciplines. Our citation analsysis offers support for Björk & Catani's suggestion that OAMJs's citation distributions can be similar to those of traditional journals, while noting considerable variation in citation rates across the eleven titles. We conclude that while the OAMJ term is useful as a means of grouping journals which share a set of key characteristics, there is no such thing as a "typical" mega-journal, and we suggest several areas for additional research that might help us better understand the current and future role of OAMJs in scholarly communication.