Combination of a heavy lift vessel and an floating appendage structure which are interconnected by a hinge having a horizontal hinge axis, wherein: - the heavy lift vessel comprises: ∘ at least one crane (15; 15A,15B) comprising a crane boom, wherein the heavy lift vessel is configured to carry out heavy lift operations by itself, i.e. without the floating appendage structure, ∘ at least one vessel hinge assembly, - the floating appendage structure is configured to lift a heavy structure at sea, the heavy structure being a topside or a substructure for supporting a topside, wherein the floating appendage structure comprises: ∘ a hull, ∘ at least one appendage hinge assembly configured to be connected to the vessel hinge assembly and to form the hinge therewith, ∘ at least one crane line connector mounted to the hull, wherein the heavy lift vessel and the floating appendage structure are interconnected via the hinge, wherein the hinge allows a rotation of the floating appendage structure relative to the heavy lift vessel about the hinge axis, and wherein a crane line suspension point of the at least one crane boom is positioned above the floating appendage structure, wherein the at least one crane is connected to the floating appendage structure, wherein at least one first crane line extends from the first crane line connector to the crane line suspension point of the at least one crane, wherein the floating appendage structure is a semi-submersible vessel, comprising: - one or more floaters, - multiple columns which extend upward from the at least one floater over a vertical distance and define open areas between the columns, and - ballasting tanks which can be filled and emptied for varying the draught of the floating appendage structure, wherein the combination comprises a passageway between the columns of the floating appendage structure and the heavy lift vessel or between the columns of the floating appendage structure, wherein the passageway is constructed to position a barge or substructure in said passageway between said columns when said columns intersect the waterline for: 1) transfer of the topside from the floating appendage structure to the barge or substructure, and/or 2) for transfer of the topside from the barge or substructure to the floating appendage structure, and/or 3) for lifting the substructure or a portion of the substructure. - the heavy lift vessel comprises: ∘ at least one crane (15; 15A,15B) comprising a crane boom, wherein the heavy lift vessel is configured to carry out heavy lift operations by itself, i.e. without the floating appendage structure, ∘ at least one vessel hinge assembly, ∘ at least one crane (15; 15A,15B) comprising a crane boom, wherein the heavy lift vessel is configured to carry out heavy lift operations by itself, i.e. without the floating appendage structure, ∘ at least one vessel hinge assembly, - the floating appendage structure is configured to lift a heavy structure at sea, the heavy structure being a topside or a substructure for supporting a topside, wherein the floating appendage structure comprises: ∘ a hull, ∘ at least one appendage hinge assembly configured to be connected to the vessel hinge assembly and to form the hinge therewith, ∘ at least one crane line connector mounted to the hull, ∘ a hull, ∘ at least one appendage hinge assembly configured to be connected to the vessel hinge assembly and to form the hinge therewith, ∘ at least one crane line connector mounted to the hull, wherein a crane line suspension point of the at least one crane boom is positioned above the floating appendage structure, wherein the at least one crane is connected to the floating appendage structure, wherein at least one first crane line extends from the first crane line connector to the crane line suspension point of the at least one crane, wherein the floating appendage structure is a semi-submersible vessel, comprising: - one or more floaters, - multiple columns which extend upward from the at least one floater over a vertical distance and define open areas between the columns, and - ballasting tanks which can be filled and emptied for varying the draught of the floating appendage structure, - one or more floaters, - multiple columns which extend upward from the at least one floater over a vertical distance and define open areas between the columns, and - ballasting tanks which can be filled and emptied for varying the draught of the floating appendage structure, 1) transfer of the topside from the floating appendage structure to the barge or substructure, and/or 2) for transfer of the topside from the barge or substructure to the floating appendage structure, and/or 3) for lifting the substructure or a portion of the substructure.