A self-expanding stent structure is provided having a main portion that expands to a first diameter and a branch portion that expands to a second diameter, different the first diameter, the main portion having a link portion that forms a flexible linkage to, and forms part of, the branch portion. The self-expanding structure may be compressed to a reduced diameter for delivery, and resumes an expanded diameter during deployment. The self-expanding stent structure also may be advantageously incorporated in an asymmetric stent-graft system. Methods of use are also provided, wherein the main portion of the self-expanding structure, when deployed in a trunk vessel, may be used to anchor the branch portion in a branch vessel.