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We present new and archival atomic hydrogen (\hi) observations of \galnum\ of the most massive spiral galaxies in the local Universe ($M_\star>10^{11} \, \mathrm{M}_\odot$). From 3D kinematic modeling of the datacubes, we derive extended \hi\ 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, $M \propto V^{4}$) and Fall relation (specific angular momentum vs mass, $j \propto M^{0.6}$), 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 $f_\mathrm{M} \equiv M_\star/M_\mathrm{h}$ and specific angular momentum $f_\mathrm{j} \equiv j_\star/j_\mathrm{h}$ and $f_\mathrm{j,bar} \equiv j_\mathrm{bar}/j_\mathrm{h}$. Combining our sample with others from the literature for less massive disc-dominated galaxies, we find that $f_\mathrm{M}$ rises monotonically with $M_\star$ and $M_\mathrm{h}$ (instead of the inverted-U shaped $f_\mathrm{M}$ for spheroid-dominated galaxies), while $f_\mathrm{j}$ and $f_\mathrm{j,bar}$ 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.