  Recently it was discovered that the ground state orbital angular momentum in
two-dimensional chiral superfluids with pairing symmetry $(p_x+ip_y)^\nu$
depends on the winding number $\nu$ in a striking manner. The ground state
value for the $\nu=1$ case is $L_z=\hbar N/2$ as expected by counting the
Cooper pairs, while a dramatic cancellation takes place for $\nu>1$. The origin
of the cancellation is associated with the topological edge states that appear
in a finite geometry and give rise to a spectral asymmetry. Here we study the
reduction of orbital angular momentum for different potential profiles and
pairing strengths, showing that the result $L_z=\hbar N/2$ is robust for
$\nu=1$ under all studied circumstances. We study how angular momentum depends
on the gap size $\Delta/E_F$ and obtain the result $L_z=\frac{\hbar\nu}{2}
N(1-\frac{\mu}{E_F})$ for $\nu=2,3$. Thus, the gap-dependence of $L_z$ for
$\nu<4$ enters at most through the chemical potential while $\nu\geq4$ is
qualitatively different. In addition, we generalize the spectral asymmetry
arguments to \emph{total} angular momentum in the ground state of triplet
superfluids where due to a spin-orbit coupling $L_z$ is not a good quantum
number. We find that the ground state total angular momentum also behaves very
differently depending on total angular momentum of the Cooper pairs.
