An apparatus comprising: a first stent graft (600, 700, 800, 1006) that is at least partially insertable into a first blood vessel, wherein the first stent graft has a first end, a second end, and an outside surface; and an inflatable fill structure (602, 702, 802, 1102) fixed to a portion of the outside surface of the first stent graft (600, 700, 800, 1006), characterised in that: the inflatable fill structure (602, 702, 802, 1102) is confined to be around the outside surface of the first stent graft (600, 700, 800, 1006) between the first end and the second end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (602, 702, 802, 1102) is in an uninflated state, and wherein the inflatable fill structure (602, 702, 802, 1102) comprises an outer membrane that is configured to extend beyond the first end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (600, 700, 800, 1006) is in a filled state, wherein the first end of the first stent graft (600, 700, 800, 1006) is configured to receive an end of a second stent graft (606, 714, 812a-b, 1110), and wherein the outer membrane is configured such that a portion of the outer membrane extends over a portion of the second stent graft (606, 714, 812a-b, 1110) when the end of the second stent graft (606, 714, 812a-b, 1110) has been received in the first end of the first stent graft (600, 700, 800, 1006) and the inflatable fill structure (602, 702, 802, 1102) is in the filled state. a first stent graft (600, 700, 800, 1006) that is at least partially insertable into a first blood vessel, wherein the first stent graft has a first end, a second end, and an outside surface; and an inflatable fill structure (602, 702, 802, 1102) fixed to a portion of the outside surface of the first stent graft (600, 700, 800, 1006), characterised in that: the inflatable fill structure (602, 702, 802, 1102) is confined to be around the outside surface of the first stent graft (600, 700, 800, 1006) between the first end and the second end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (602, 702, 802, 1102) is in an uninflated state, and wherein the inflatable fill structure (602, 702, 802, 1102) comprises an outer membrane that is configured to extend beyond the first end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (600, 700, 800, 1006) is in a filled state, wherein the first end of the first stent graft (600, 700, 800, 1006) is configured to receive an end of a second stent graft (606, 714, 812a-b, 1110), and wherein the outer membrane is configured such that a portion of the outer membrane extends over a portion of the second stent graft (606, 714, 812a-b, 1110) when the end of the second stent graft (606, 714, 812a-b, 1110) has been received in the first end of the first stent graft (600, 700, 800, 1006) and the inflatable fill structure (602, 702, 802, 1102) is in the filled state. the inflatable fill structure (602, 702, 802, 1102) is confined to be around the outside surface of the first stent graft (600, 700, 800, 1006) between the first end and the second end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (602, 702, 802, 1102) is in an uninflated state, and wherein the inflatable fill structure (602, 702, 802, 1102) comprises an outer membrane that is configured to extend beyond the first end of the first stent graft (600, 700, 800, 1006) when the inflatable fill structure (600, 700, 800, 1006) is in a filled state, wherein the first end of the first stent graft (600, 700, 800, 1006) is configured to receive an end of a second stent graft (606, 714, 812a-b, 1110), and wherein the outer membrane is configured such that a portion of the outer membrane extends over a portion of the second stent graft (606, 714, 812a-b, 1110) when the end of the second stent graft (606, 714, 812a-b, 1110) has been received in the first end of the first stent graft (600, 700, 800, 1006) and the inflatable fill structure (602, 702, 802, 1102) is in the filled state.