A stent graft system for intraluminal deployment in an aorta and a branch vessel that includes an aorta stent graft for deployment within the aorta and defining a lumen for the passage of blood therethrough, and having a fenestration positioned and sized so as to allow blood to flow to a contiguous branch vessel. The system also includes a branch vessel prosthesis, preferably a stent graft, having a tubular portion and a flaring portion, such that, when deployed, the flaring portion is located within the lumen of the aorta stent graft and the tubular portion passes through the fenestration and into the branch vessel. A balloon expansion catheter expands the tubular portion and flare the flaring portion. The expansion of the tubular portion and the flaring of the flaring portion may occur sequentially or simultaneously.