  (Abridged) Specific angular momentum is one of the key parameters that
control the evolution of galaxies. We derive the baryonic specific angular
momentum of disc galaxies and study its relation with the dark matter specific
angular momentum. Using a combination of high-quality HI rotation curves and
HI/near-IR surface densities, we homogeneously measure the stellar ($j_{\rm
*}$) and gas ($j_{\rm gas}$) specific angular momenta for a large sample of
local disc galaxies. This allows us to determine the baryonic specific angular
momentum ($j_{\rm bar}$) with high accuracy and across a very wide range of
masses. The $j_{\ast}-M_\ast$ relation is an unbroken power-law from $7
\lesssim$ log($M_\ast$/$M_\odot) \lesssim 11.5$, with slope $0.54 \pm 0.02$.
For the gas component, we find that the $j_{\rm gas}-M_{\rm gas}$ relation is
also an unbroken power-law from $6 \lesssim$ log($M_{\rm gas}$/$M_\odot)
\lesssim 11$, with a steeper slope of $1.02 \pm 0.04$. Regarding the baryonic
relation, our data support a correlation characterized by single power-law with
slope $0.60 \pm 0.02$. Our most massive spirals and smallest dwarfs lie along
the same $j_{\rm bar}-M_{\rm bar}$ sequence. While the relations are tight and
unbroken, we find internal correlations inside them: At fixed $M_\ast$,
galaxies with larger $j_\ast$ have larger disc scale lengths, and at fixed
$M_{\rm bar}$, gas-poor galaxies have lower $j_{\rm bar}$ than expected. We
estimate the retained fraction of baryonic specific angular momentum, finding
it constant across our entire mass range with a value of $\sim 0.6$, indicating
that the $j_{\rm bar}$ of present-day disc galaxies is comparable to the
initial specific angular momentum of their dark matter haloes. These results
set important constraints for hydrodynamical simulations and semi-analytical
models aiming to reproduce galaxies with realistic specific angular momenta.
