The modeling-by-composition paradigm can be a powerful tool in modern animation pipelines. We propose two novel interactive techniques to compose 3D assets that enable the artists to freely remove, detach and combine components of organic models. The idea behind our methods is to preserve most of the original information in the input characters and blend accordingly where necessary. The first method, QuadMixer, provides a robust tool to compose the quad layouts of watertight pure quadrilateral meshes, exploiting the boolean operations defined on triangles. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving the shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. The resulting meshes preserve the originally designed edge flows that, by construction, are captured and incorporated into the new quads. SkinMixer extends this approach to compose skinned models, taking into account not only the surface but also the data structures for animating the character. We propose a new operation-based technique that preserves and smoothly merges meshes, skeletons, and skinning weights. The retopology approach of QuadMixer is extended to work on quad-dominant and arbitrary complex surfaces. Instead of relying on boolean operations on triangle meshes, we manipulate signed distance fields to generate an implicit surface. The results preserve most of the information in the input assets, blending accordingly in the intersection regions. The resulting characters are ready to be used in animation pipelines. Given the high quality of the results generated, we believe that our methods could have a huge impact on the entertainment industry. Integrated into current software for 3D modeling, they would certainly provide a powerful tool for the artists. Allowing them to automatically reuse parts of their well-designed characters could lead to a new approach for creating models, which would significantly reduce the cost of the process.