Understanding the size, shape and morphological transformations that may occur under different temperature conditions is vital to ensuring the long term stability of metal nanoparticle catalysts. This information can be conveniently captured in a nanoscale phase diagram, that maps the thermally stable structure as a function of size. This paper presents results of theoretical modeling, based on first principle computer simulations, exploring the equilibrium and non-equilibrium morphologies of palladium nanoparticles over the entire nanoscale. A total of 18 different ideal and imperfect structures and shapes are considered and compared, to reveal a delicate balance between the sphericity, the degree of twinning, and the surface anisotropy. The phase diagram is then discussed in relation to the experiments reported in the literature.