We present new and archival atomic hydrogen (H I) observations of 15 of the most massive spiral galaxies in the local Universe (M_⋆ > 10¹¹ M_⊙). From 3D kinematic modeling of the datacubes, we derive extended H I rotation curves, and from these, we estimate masses of the dark matter halos and specific angular momenta of the discs. We confirm that massive spiral galaxies lie at the upper ends of the Tully-Fisher relation (mass vs velocity, M∝V⁴) and Fall relation (specific angular momentum vs mass, j∝M^0.6), in both stellar and baryonic forms, with no significant deviations from single power laws. We study the connections between baryons and dark matter through the stellar (and baryon)-to-halo ratios of mass f_M ≡ M_⋆/M_h and specific angular momentum f_{j, ⋆} ≡ j_⋆/j_h and f_{j, bar} ≡ j_bar/j_h. Combining our sample with others from the literature for less massive disc-dominated galaxies, we find that f_M rises monotonically with M_⋆ and M_h (instead of the inverted-U shaped f_M for spheroid-dominated galaxies), while f_{j, ⋆} and f_{j, bar} are essentially constant near unity over four decades in mass. Our results indicate that disc galaxies constitute a self-similar population of objects closely linked to the self-similarity of their dark halos. This picture is reminiscent of early analytical models of galaxy formation wherein discs grow by relatively smooth and gradual inflow, isolated from disruptive events such as major mergers and strong AGN feedback, in contrast to the more chaotic growth of spheroids.