We contribute a novel algorithm for the digitation of complete 3D object models that requires little preparation effort from the user. Notably, the presented algorithm, Joint Alignment and Stitching of Non-Overlapping Meshes (JASNOM), completes 3D object models by aligning and stitching two 3D meshes by the boundaries and does not require any previous registration between them. JASNOM only requirement is the lack of overlap between meshes, which is simple to achieve in most man made object. JASNOM takes advantage that both meshes can only be connected by their boundary to reframe the alignment problem as a search of the best assignment between boundary vertices. To make the problem tractable, JASNOM reduces the search space considerably by imposing strong constraints on valid assignments that transform the original combinatorial problem into a discrete linear problem. By not requiring previous camera registration and by not depending on shape features, JASNOM contributions range from quick modeling of 3D objects to hole filling in meshes.