  We investigate the origin of the observed scaling $j\sim R^{3/2}$ between the
specific angular momentum $j$ and the radius $R$ of molecular clouds (MCs) and
their their substructures, and of the observed near independence of $\beta$,
the ratio of rotational to gravitational energy, from $R$. To this end, we
measure the angular momentum (AM) of sets of particles in an SPH simulation of
the formation, collapse and fragmentation of giant MCs. The sets of SPH
particles are defined either as ``clumps'' (connected particle sets), or as
lagrangian sets that conform a connected clump only at a certain time $\tdef$.
We find that: {\it i)} Clumps evolve along the observed \jR\ relation at all
times, {\it ii)} Lagrangian particle sets evolve along the observed relation
when the volume containing them also contains a large number of other
``intruder'' particles. Otherwise, they evolve with $j\sim$ cst. {\it iii)}
Tracking lagrangian sets to the future, we find that a subset of the SPH
particles participates in the collapse, while another disperses away. {\it iv)}
Noting that, under AM conservation, $\beta$ increases during contraction, we
suggest that its near independence of radius may arise from the competition
between this increase and an increase in the AM exchange rate at higher
rotational energy density gradient. {\it v)} We suggest that, if MCs are
globally dominated by gravity, the observed \jR\ relation arises because the
observational selection of its dense structures amounts to selecting the
fragments that have lost AM via Reynolds stresses from their neighbors.
