A system and method for endoluminal grafting of a main anatomic conduit in its diseased state in which it dilates to pose a life threatening condition and its various conduits that emanate from the main anatomic conduit. The grafting system comprises an endoaortic graft having at least one opening therein and at least one branch graft that is passable through the opening of the endoaortic graft into the branch anatomic conduit(s) such that the junction between the branch graft and the endoaortic graft is substantially fluid tight. A system and method for delivery of the endoaortic graft and also a system and method for efficient alignment and deployment of the branch (e.g., side branch) graft such that the coupling of the branch graft with the endoaortic graft is efficient and exact and fluid-tight; and a system and method for coupling the branch to the endoaortic graft via a coupling mechanism employing a memory metal alloy; a system and method for the proper and exact alignment of the endoaortic graft and the branch using magnetic force of a suitable nature, and which does not use the magnetic force as the coupling mechanism.