This paper presents a new Self-organizing Map suitable for recovering a 2D surface starting from points sampled on the object surface. Growing self-organizing surface map (GSOSM), is a new algorithm of the growing SOM family that reproduce the surface as an incremental mesh composed of triangles which are approximately equilateral. GSOSM introduces a new connection learning rule, called competitive connection Hebbian learning (CCHL), that produces a complete triangulation where CHL fails. Differently from other models such as neural meshes (NM), GSOSM recovers a surface topology from homogeneous samples distribution according to any presentation sequence. GSOSM map is a mesh that represents the object surface with a detail level established by a parameter, allowing different versions of a same object surface. Moreover, GSOSM reconstructions are very often meshes free of false or overlapping faces, and then GSOSM is a potential tool for virtual reconstruction of real objects.