A method of transporting an undersea structure for supporting and anchoring offshore equipment, preferably a wind turbine, and for depositing it on the sea bottom, said undersea support and anchoring structure comprising a gravity base comprising a first solid block or a first hollow caisson filled with ballast means and that rests on the sea bottom and provides anchoring by virtue of its weight; said gravity first block or caisson having a top outer surface supporting a column and/or a top device suitable for receiving the base of the pylon of a wind turbine, a plane bottom surface suitable for resting on the sea bottom, and a preferably leakproof outside surface, in which method the following steps are performed: a) stowing said base while fitted with buoyancy elements; and then b) lowering said base to the sea bottom; and wherein: - before step a), a plurality of hollow buoyancy and ballasting second caissons (3-1, 3-2) are releasably fastened on the outside surface (2a, 2b, 2c) of said gravity first block or first caisson; and - in step a), at least some of said second caissons (3, 3-1, 3-2) are emptied at least in part; and - in step b), sea water is added into said second caissons (3, 3-1, 3-2) in order to lower said base down to the sea bottom, with said second caissons (3, 3-1, 3-2) preferably remaining filled only in part with sea water; and - after step b), said second caissons (3, 3-1, 3-2) are separated and emptied, preferably progressively, so as to raise them to the surface by buoyancy, preferably progressively; the method being characterized in that: - a plurality of said second caissons (3-1, 3-2) having the same shape and the same dimensions are fastened on an outside surface of frustoconical shape of the first block or first caisson in a symmetrical distribution relative to a plane of symmetry of said first block or caisson and containing the axis of revolution (ZZ') of the first block or first caisson, the outside surfaces and the inside surfaces of said second caissons defining surfaces of revolution of frustoconical shape having the same axis of revolution (ZZ') as said outside surface of said first block or first caisson; - each said second caisson having an inside surface matching the shape of the facing portion of said outside surface (2a, 2b, 2c) of the first block or caisson against which it is applied, said second caissons (3-1, 3-2) being arranged in such a manner that together said second caissons cover all of said outside surface, each said second caisson (3-1, 3-2) having at least one valve opening to the outside; and - the distance (d) between said inside and outside surfaces (3a, 3b) of said second caissons is less than 1/3 of their height in the direction of their height (h) in the axial direction ZZ'; and - in step b), the base is lowered by controlling solely the filling of said second caissons. a) stowing said base while fitted with buoyancy elements; and then b) lowering said base to the sea bottom; - before step a), a plurality of hollow buoyancy and ballasting second caissons (3-1, 3-2) are releasably fastened on the outside surface (2a, 2b, 2c) of said gravity first block or first caisson; and - in step a), at least some of said second caissons (3, 3-1, 3-2) are emptied at least in part; and - in step b), sea water is added into said second caissons (3, 3-1, 3-2) in order to lower said base down to the sea bottom, with said second caissons (3, 3-1, 3-2) preferably remaining filled only in part with sea water; and - after step b), said second caissons (3, 3-1, 3-2) are separated and emptied, preferably progressively, so as to raise them to the surface by buoyancy, preferably progressively; - a plurality of said second caissons (3-1, 3-2) having the same shape and the same dimensions are fastened on an outside surface of frustoconical shape of the first block or first caisson in a symmetrical distribution relative to a plane of symmetry of said first block or caisson and containing the axis of revolution (ZZ') of the first block or first caisson, the outside surfaces and the inside surfaces of said second caissons defining surfaces of revolution of frustoconical shape having the same axis of revolution (ZZ') as said outside surface of said first block or first caisson; - each said second caisson having an inside surface matching the shape of the facing portion of said outside surface (2a, 2b, 2c) of the first block or caisson against which it is applied, said second caissons (3-1, 3-2) being arranged in such a manner that together said second caissons cover all of said outside surface, each said second caisson (3-1, 3-2) having at least one valve opening to the outside; and - the distance (d) between said inside and outside surfaces (3a, 3b) of said second caissons is less than 1/3 of their height in the direction of their height (h) in the axial direction ZZ'; and - in step b), the base is lowered by controlling solely the filling of said second caissons.