We have studied pattern regulation in the medial-lateral axis of the insect segment by grafting legs of beetle larvae (Tenebrio molitor) in different orientations into different positions medial and lateral to the leg site. The Boundary Model and Polar Coordinate Model of the insect appendage predict various patterns of supernumerary leg regeneration, and these grafts were designed to test the predictions. When a larval leg is grafted with normal anterior-posterior orientation medial to the normal leg, larvae and subsequent adults bear the graft plus a supernumerary leg. This is located where the lateral edge of the grafted leg confronted medial thorax (from the leg base across to the midline) and is orientated as a mirror image of the graft. The tarsal structure of supernumeraries resulting from grafts of the mesothoracic leg onto the metathorax shows that the supernumeraries may be derived from the graft, the host site or from both sources. Similarly, when a leg is grafted lateral to the leg site, a supernumerary forms at the confrontation between the medial edge of the graft and lateral thorax (from leg base across to the dorsal tergite). These results agree with the predictions of both models and would indicate that the compartments or the positional values extend out from the leg to the midline and the edge of the tergite. The two models differ in their predictions for the number, position and orientation of supernumeraries following 180 degree rotation of the grafted leg. When the rotated graft is placed lateral to the leg, larvae and adults form a single supernumerary which, in accordance with the Polar Coordinate Model, is lateral to the graft and orientated as a mirror image of it. However, the results of the corresponding medial graft cannot be readily explained by either model. Larvae form a single supernumerary either posterior or medial to the graft, suggesting a modified model with unequally spaced positional values, but the subsequent adult supernumeraries are almost all located medially. Experiments involving a graft placed medial to the leg site frequently show duplication of the adult midline suture, an extra branch forming between the thorax and the graft or supernumerary leg. In this case, as in the regeneration of the dorsal midline, the extreme medial structure is formed between two more lateral regions, which need not come from opposite sides of the body, but must have opposite mediolateral polarities. At present, no model can adequately explain all the results of grafting and extirpation on the insect ventral thorax.