Reconstructing tubular structures with high-order branching is a difficult task to perform automatically. Medical applications in particular demand accurate models of such objects that fulfill specific topological and geometric criteria. Indeed, the reconstructed object should be a 2-manifold surface with compact, adaptive geometry. We present a generic algorithm for automatically reconstructing n-furcated tubular surfaces. Our approach relies on a strong underlying topological structure and a novel n-furcation reconstruction algorithm using convex entities.