A floating petroleum production support supporting or suitable for supporting bottom-to-surface connection pipes between a plurality of undersea pipes resting on the seabed and the said floating support on the surface, said floating support including a turret having a cavity immersed at least in part within a structure offset to the front of the floating support or incorporated in or under the hull of the floating support, preferably passing through the hull of the floating support over its entire height, said turret comprising a cylindrical internal structure, preferably of circular section, within said cavity, said internal structure comprising a tubular side wall surmounted at its top end by a top platform coming substantially to the level of the deck of the floating support, said tubular side wall being closed at least in part at its bottom end by a bottom wall, said cylindrical internal structure passing or being suitable for passing a plurality of flexible first pipes (4, 4a-4c) connected to said top platform and extending under said bottom wall to undersea pipes resting on the sea bottom or to second pipes themselves connected to undersea pipes resting on the sea bottom, said cylindrical internal structure being mounted to rotate relative to said cavity and said hull via rotary guide elements, preferably at least one rolling or friction bearing (2a 1, 2a 2, 2a 3), in such a manner as to allow said floating support to rotate about a substantially vertical axis ZZ' of the cavity of said turret without causing a portion of said turret to rotate relative to the same vertical axis ZZ', the floating support being characterized in that said internal cylindrical structure comprises at least one, and preferably a plurality of preferably rigid guide and offset pipes containing and guiding or suitable for containing and guiding a said flexible first pipe, said guide pipe passing through said bottom wall and passing non-vertically inside said cylindrical internal structure of the turret between: • firstly said bottom wall at a first location of said bottom wall where said guide pipe is fastened, said first location being preferably located at the periphery of said bottom wall; and • secondly an internal platform secured to said internal cylindrical structure above said bottom wall and above the level of the water surface, the top end of said guide pipe being fastened to said internal platform at a second location where the top end of said flexible pipe contained in said guide pipe is fastened or is suitable for being fastened, said second location not being in vertical alignment with said first location, said second location preferably being arranged at the periphery of said internal platform. • firstly said bottom wall at a first location of said bottom wall where said guide pipe is fastened, said first location being preferably located at the periphery of said bottom wall; and • secondly an internal platform secured to said internal cylindrical structure above said bottom wall and above the level of the water surface, the top end of said guide pipe being fastened to said internal platform at a second location where the top end of said flexible pipe contained in said guide pipe is fastened or is suitable for being fastened, said second location not being in vertical alignment with said first location, said second location preferably being arranged at the periphery of said internal platform.