Aims. Specific angular momentum (the angular momentum per unit mass, j = J/M) is one of the key parameters that control the evolution of galaxies, and it is closely related with the coupling between dark and visible matter. In this work, we aim to derive the baryonic (stars plus atomic gas) specific angular momentum of disc galaxies and study its relation with the dark matter specific angular momentum.Methods. Using a combination of high-quality H I rotation curves, H I surface densities, and near-infrared surface brightness profiles, we homogeneously measure the stellar (j*) and gas (jgas) specific angular momenta for a large sample of nearby disc galaxies. This allows us to determine the baryonic specific angular momentum (jbar) with high accuracy and across a very wide range of masses.Results. We confirm that the j* − M* relation is an unbroken power-law from 7 ≲ log(M*/M⊙) ≲ 11.5, with a slope 0.54 ± 0.02, setting a stronger constraint at dwarf galaxy scales than previous determinations. Concerning the gas component, we find that the jgas − Mgas relation is also an unbroken power-law from 6 ≲ log(Mgas/M⊙) ≲ 11, with a steeper slope of 1.02 ± 0.04. Regarding the baryonic relation, our data support a correlation characterized by a single power-law with a slope 0.60 ± 0.02. Our analysis shows that our most massive spirals and smallest dwarfs lie along the same jbar − Mbar sequence. While the relations are tight and unbroken, we find internal correlations inside them: At fixed M*, galaxies with larger j* have larger disc scale lengths, and at fixed Mbar, gas-poor galaxies have lower jbar than expected. We estimate the retained fraction of baryonic specific angular momentum, fj, bar, finding it constant across our entire mass range with a value of ∼0.6, indicating that the baryonic specific angular momentum of present-day disc galaxies is comparable to the initial specific angular momentum of their dark matter haloes. In general, these results set important constraints for hydrodynamical simulations and semi-analytical models that aim to reproduce galaxies with realistic specific angular momenta.Key words: galaxies: kinematics and dynamics / galaxies: formation / galaxies: fundamental parameters / galaxies: evolution / galaxies: dwarf / galaxies: spiral⋆ Full Table 1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/647/A76