Abstract: Anastomotic methods and devices for placing a target vessel in fluid communication with a target vessel. A conduit includes an attachment portion adapted to be secured to a target vessel in fluid communication with the lumen of the vessel. The target vessel wall is sandwiched between first and second components of the attachment portion to provide both a secure and sealed connection. One component is placed in the vessel lumen against the interior surface of the wall and has an outlet that directs blood into the target vessel. This component is elongated, e.g., elliptical or rectangular, such that a minimum amount of material is present at the outlet. This results in the outlet having a diameter that substantially maintains much of the cross-sectional area of the native target vessel.