  We study the physical processes inducing the alignment of the grain axis of
maximum inertia moment with the angular momentum (${\bf J}$, i.e., internal
alignment) and of ${\bf J}$ with the magnetic field (i.e., external alignment)
of very large grains (VLGs, of radius $a>10\mu$m) using the grain alignment
framework based on radiative torques (RATs) and mechanical torques (METs). We
derive analytical formulae for critical sizes of grain alignment, assuming that
grains are aligned at both low$-J$ and high$-J$ attractors by RATs (METs). For
protostellar cores, we find that super-Barnett relaxation can induce efficient
internal alignment for VLGs with large iron inclusions aligned at high$-J$
attractors by RATs (METs). In contrast, inelastic relaxation can be efficient
for VLGs made of any composition. For external alignment, we find that VLGs
with iron inclusions aligned at high$-J$ attractors can have magnetic alignment
by RATs ($B-$RAT) or METs ($B-$ MET), enabling dust polarization as a reliable
tracer of magnetic fields in such dense regions. Still, grains at low$-J$
attractors or grains without iron inclusions have alignment along the radiation
direction ($k-$RAT) or gas flow ($v-$MET). For protostellar disks, we find that
super-Barnett relaxation can be efficient for grains with large iron inclusions
in the outer disk thanks to spinup by METs, but inelastic relaxation is
inefficient. VLGs aligned at low-J attractors can have $k-$RAT ($v-$MET)
alignment, but grains aligned at high$-J$ attractors have likely $B-$RAT
($B-$MET) alignment. Grain alignment by METs appears to be more important than
RATs in protostellar disks.
