The umbilical of Remote Operated Vehicle (ROV) has two main problems: it is subject to entanglement with obstacles or itself, and its shape is difficult to predict for navigation. To address these issues, this article proposes a passive self-management of an ROV's umbilical by adding one or two elements, like ballasts, buoys, or an oriented thruster, to stretch it and gives it a predictable shape. These elements can be fixed or move freely on the umbilical. In opposite with previous works, we propose a general model which can estimate the shape of the umbilical in three-dimensions regardless of the orientation of the force applied to the elements, allowing to consider the presence of underwater currents, passive or motorized elements on the tether, and the presence or absence of TMS. Several examples of umbilical configurations are proposed, each one adapted for ROV exploration in various environments, including near-surface, seafloor, near-wall, and dive between obstacles. The model is compared with results proposed in other works. The limits of the method are discussed.