One of the major events in animal morphogenesis is the emergence of a polar body axis. Here, we combine classic grafting techniques with live imaging to explore the plasticity of polarity determination during whole body regeneration in Hydra. Composite tissues are made by fusing two rings, excised from separate animals, in different configurations that vary in the polarity and original positions of the rings along the body axes of the parent animals. Under frustrating initial configurations, body axis polarity that is otherwise stably inherited from the parent animal, can become labile and even be reversed. Importantly, the site of head regeneration exhibits a strong bias toward the edges of the tissue, even when this involves polarity reversal. In particular, we observe head formation at an originally aboral tissue edge, which is not compatible with models of Hydra regeneration based only on preexisting morphogen gradients or an injury response. The site of the new head invariably contains an aster-like defect in the organization of the supra-cellular ectodermal actin fibers. While a defect is neither required nor sufficient for head formation, we show that the defect at the new head site can arise via different routes, either appearing directly following excision as the tissue seals at its edge or through de novo defect formation at the fusion site. Altogether, our results show that the emergence of a polar body axis depends on the original polarity and position of the excised tissues as well as structural factors, suggesting that axis determination is an integrated process that arises from the dynamic interplay of multiple biochemical and mechanical processes.