Poisson-Dirac branes in Poisson-Sigma models

We analyse the general boundary conditions (branes) consistent with the Poisson-sigma model and study the structure of the phase space of the model defined on the strip with these boundary conditions. Finally, we discuss the perturbative quantization of the model on the disc with a Poisson-Dirac brane and relate it to Kontsevich's formula for the deformation quantization of the Dirac bracket induced on the brane.