In this work, a computational procedure is proposed to vascularize anatomical regions supplied by many inflow sites. The proposed methodology creates a partition of the territory to be vascularized into nonoverlapping subdomains that are independently supplied by the so-called perforator arteries (inflow sites). Then, in each subdomain, the constrained constructive optimization method is used to generate a network of vessels. The identification of subdomains in a certain vascular territory perfused by many perforator arteries turns out to be a fundamental problem towards understanding the morphological conformation of peripheral beds in the cardiovascular system. The methodology is assessed through two academic examples showing the main structural features of the so-defined vascular territory partition and the corresponding arterial networks. In addition, the vascularization of a three-dimensional sheet-like tissue is presented with potential application in flap planning and design. Copyright © 2013 John Wiley & Sons, Ltd.