Anastomotic components may be attached to hollow bodies or vessels by magnetic or mechanical force to create an anastomosis, form a port in a vessel, or repair a diseased vessel lumen. Anastomoses are created by coupling a first connection to an end of a vessel and then attracting it to a second connector secured to the side wall of another vessel. The connection between the first and second connectors may be solidly magnetic, solely mechanical, or a combination thereof. Also disclosed are methods and devices for treating diseased vessel lumens, for example abdominal aortic aneurysm. A plurality of docking members is attached to the vessel at solicited positions, and then one or more grafts is secured to the docking members in any suitable manner.