A method for installing a tension leg platform based floating object at a plurality of anchor points at sea using an installation vessel and a remotely operated underwater vehicle, ROV; the floating object comprising a central body and at least three buoyancy assemblies positioned around the central body in a horizontal plane, with each of the buoyancy assemblies at least connected to the central body and adapted to be connected to an associated one of the anchor points, the method comprising: • attaching a mooring leg comprising at least one mooring line at each anchor point; • for each anchor point connecting a pull-down line between each buoyancy assembly and its associated anchor point; • tensioning the pull-down lines such that the floating object is lowered with respect to the water surface to an installation elevation level below an operational elevation level; • for each anchor point connecting the mooring leg with the associated buoyancy assembly while the mooring leg is in slack mode, • after connecting the mooring lines with the buoyancy assemblies, paying out the pull-down lines to transfer load to the mooring legs such that the floating object rises upward from the installation elevation level to the operational elevation level where the mooring legs are in tensioned mode. anchor points at sea using an installation vessel and a remotely operated underwater vehicle, ROV; the floating object comprising a central body and at least three buoyancy assemblies positioned around the central body in a horizontal plane, with each of the buoyancy assemblies at least connected to the central body and adapted to be connected to an associated one of the anchor points, the method comprising: • attaching a mooring leg comprising at least one mooring line at each anchor point; • for each anchor point connecting a pull-down line between each buoyancy assembly and its associated anchor point; • tensioning the pull-down lines such that the floating object is lowered with respect to the water surface to an installation elevation level below an operational elevation level; • for each anchor point connecting the mooring leg with the associated buoyancy assembly while the mooring leg is in slack mode, • after connecting the mooring lines with the buoyancy assemblies, paying out the pull-down lines to transfer load to the mooring legs such that the floating object rises upward from the installation elevation level to the operational elevation level where the mooring legs are in tensioned mode. • attaching a mooring leg comprising at least one mooring line at each anchor point; • for each anchor point connecting a pull-down line between each buoyancy assembly and its associated anchor point; • tensioning the pull-down lines such that the floating object is lowered with respect to the water surface to an installation elevation level below an operational elevation level; • for each anchor point connecting the mooring leg with the associated buoyancy assembly while the mooring leg is in slack mode, • after connecting the mooring lines with the buoyancy assemblies, paying out the pull-down lines to transfer load to the mooring legs such that the floating object rises upward from the installation elevation level to the operational elevation level where the mooring legs are in tensioned mode.