  Colored tensor models have been recently shown to admit a large N expansion,
whose leading order encodes a sum over a class of colored triangulations of the
D-sphere. The present paper investigates in details this leading order. We show
that the relevant triangulations proliferate like a species of colored trees.
The leading order is therefore summable and exhibits a critical behavior,
independent of the dimension. A continuum limit is reached by tuning the
coupling constant to its critical value while inserting an infinite number of
pairs of D-simplices glued together in a specific way. We argue that the
dominant triangulations are branched polymers.
