We take the first steps in a systematic study of Group Field Theory
renormalization, focusing on the Boulatov model for 3D quantum gravity. We
define an algorithm for constructing the 2D triangulations that characterize
the boundary of the 3D bubbles, where divergences are located, of an arbitrary
3D GFT Feynman diagram. We then identify a special class of graphs for which a
complete contraction procedure is possible, and prove, for these, a complete
power counting. These results represent important progress towards
understanding the origin of the continuum and manifold-like appearance of
quantum spacetime at low energies, and of its topology, in a GFT framework