A device comprising a rigid support structure held immersed in the subsurface by floats and anchored to the bottom of the sea by tension legs, for the purpose of supporting a plurality of arch-shaped support and guide elements, referred to as "troughs", in a bottom-to-surface connection installation between a single floating support and the bottom of the sea, the installation having a plurality of flexible lines comprising flexible pipes (1, 1a, 1b) extending to the bottom of the sea where they are connected to wellheads, to equipment, or to the ends of undersea pipes resting on the sea bottom, said flexible lines being supported respectively by said plurality of troughs, in which device: • said trough support structure is connected to a base resting on and/or anchored to the sea bottom by a plurality of n tension legs tensioned substantially in parallel, preferably substantially vertically, by said floats, where n is not less than six, each of a plurality of p said tension legs from the n tension legs, where p is not less than (n-2), being connected at one of its ends (7a, 7b) to a distance-varying device, said distance-varying device being connected to said base or to said support structure or being integral with said base or said support structure, the other end of said tension leg being fastened to an attachment point secured to said support structure or respectively to said base, said distance-varying device being suitable for being actuated to vary the distance between its attachment point to said tension leg and said base or said support structure to which it is fastened or connected; and • the top end of said tension leg is fastened at a top attachment point secured to said support structure or respectively to said distance-varying device, the bottom end of said tension leg being fastened at a bottom attachment point secured to said distance-varying device or respectively to said base, said distance-varying device being suitable for: • varying the distance between (i) said top attachment point and said support structure when said distance-varying device is secured to said support structure; or • varying the distance between (i) a said bottom attachment point and said base when said distance-varying device is secured to said base; the device being characterized in that said support structure presents a longitudinal shape of substantially rectangular horizontal section, that is preferably substantially symmetrical about a longitudinal vertical midplane, the device having at least six tension legs, each connected to a said distance-varying device, and said support structure has at least six top attachment points, with four of the top attachment points (7a1, 7a2, 7a5, 7a6) defining the four corners of a rectangle, the other two top attachment points (7a3, 7a4) being arranged inside a circle that circumscribes said rectangle, at or in the vicinity of two long sides of the rectangle, the four corner attachment points (7a1, 7a2, 7a5, 7a6) being arranged in the proximity of the longitudinal ends of said support structure. • said trough support structure is connected to a base resting on and/or anchored to the sea bottom by a plurality of n tension legs tensioned substantially in parallel, preferably substantially vertically, by said floats, where n is not less than six, each of a plurality of p said tension legs from the n tension legs, where p is not less than (n-2), being connected at one of its ends (7a, 7b) to a distance-varying device, said distance-varying device being connected to said base or to said support structure or being integral with said base or said support structure, the other end of said tension leg being fastened to an attachment point secured to said support structure or respectively to said base, said distance-varying device being suitable for being actuated to vary the distance between its attachment point to said tension leg and said base or said support structure to which it is fastened or connected; and • the top end of said tension leg is fastened at a top attachment point secured to said support structure or respectively to said distance-varying device, the bottom end of said tension leg being fastened at a bottom attachment point secured to said distance-varying device or respectively to said base, said distance-varying device being suitable for: • varying the distance between (i) said top attachment point and said support structure when said distance-varying device is secured to said support structure; or • varying the distance between (i) a said bottom attachment point and said base when said distance-varying device is secured to said base; the device being characterized in that said support structure presents a longitudinal shape of substantially rectangular horizontal section, that is preferably substantially symmetrical about a longitudinal vertical midplane, the device having at least six tension legs, each connected to a said distance-varying device, and said support structure has at least six top attachment points, with four of the top attachment points (7a1, 7a2, 7a5, 7a6) defining the four corners of a rectangle, the other two top attachment points (7a3, 7a4) being arranged inside a circle that circumscribes said rectangle, at or in the vicinity of two long sides of the rectangle, the four corner attachment points (7a1, 7a2, 7a5, 7a6) being arranged in the proximity of the longitudinal ends of said support structure.