Stephen Pinfield et al. have self-archived "Open-Access Repositories Worldwide, 2005-2012: Past Growth, Current Characteristics and Future Possibilities" in White Rose Research Online.
Here's an excerpt:
This paper reviews the worldwide growth of open-access (OA) repositories, December 2005 to December 2012, using data collected by the OpenDOAR project. It shows that initial repository development was focused on North America, Western Europe and Australasia, particularly the USA, UK, Germany and Australia. Soon after, Japan increased its repository numbers. Since 2010, other geographical areas and countries have seen repository growth, including East Asia (especially Taiwan), South America (especially Brazil) and Eastern Europe (especially Poland). During the whole period, countries such as France, Italy and Spain have maintained steady growth, whereas countries such as China and Russia have experienced relatively low levels of growth. Globally, repositories are predominantly institutional, multidisciplinary and English-language-based. They typically use open-source OAI-compliant repository software but remain immature in terms of explicit licensing arrangements. Whilst the size of repositories is difficult to assess accurately, the available data indicate that a small number of large repositories and a large number of small repositories make up the repository landscape. These trends and characteristics are analyzed using Innovation Diffusion Theory (IDT) building on previous studies. IDT is shown to provide a useful explanatory framework for understanding repository adoption at various levels: global, national, organizational and individual. Major factors affecting both the initial development of repositories and their take up by users are identified, including IT infrastructure, language, cultural factors, policy initiatives, awareness-raising activity and usage mandates. It is argued that mandates in particular are likely to play a crucial role in determining future repository development.