OK, decades since I've crunched some of these equations, so thanks for
the refresher.

How about this example:

at (0,0,0) I have a SMBH at the center of a galaxy.

The galaxy is purely a disk of stars in the XY plane, with rotation
about the Z axis. Right hand rule, thumb North, fingers show stellar
rotation direction. Disk is thin, call it 1pc compared to 50kpc radius
for the disk.

Now, I drop a bunch of stars from N and S of the SMBH. They fall onto
different sides of the SMBH, AND, they thermalize with the disk stars.

Seems to me I will form a central bulge where initially none existed.

From your comments (which make sense), the net angular momentum of the
system will not change. But where I'm still confused, is how the sum of
angular momentum of the in falling material, adds to the disk rotation
angular momentum.

for the disk material, the angular momentum vector is in the north Z
direction. For the infalling material, the angular momentum vector for
each in falling star is in the XY plane, orthogonal to the disk
material.

As the infalling material "thermalizes" with the disk stars, a central
bulge will form with random motions..........but I am not sure how the
Net becomes changed or if it does.

If the infalling material falls in equally on all sides of the central
SMBH, then, it must have zero angular momentum. Therefore by your
comments, (which make sense) the resultant bulge must have a net angular
momentum that's still along the Z axis north.

right?

rt