Research communities from high energy physics to humanities utilised grid infrastructures to support and accelerate their research. Their computations can be executed by different grid technologies: Grids of cluster systems, like the German D-Grid, grids of supercomputers, like the Distributed European Infrastructure for Supercomputing Applications (DEISA), or desktop grids consolidated in the International Desktop Grid Federation (IDGF). UNICORE is one of the three grid middleware environments supported by the European Middleware Initiative (EMI) for managing a set of cluster or supercomputers, but desktop grids are currently unsupported. This work fills this gap enabling UNICORE to support all three kinds of grid technologies of the European Grid Infrastructure (EGI). This unified interface enables European scientists to access web services, portals, and applications on all grid technologies in the same way.