When vignetting occurs, the usual problem with a condenser lens set is that the projected light is concentrated into too narrow of a beam for the intended negative size.
A condenser assembly projects light in a fixed converging beam that’s intended to concentrate the light into a uniformly illuminated circle not much larger than the diagonal of the format for which it’s intended. In this respect, a condenser set behaves very much like a magnifying hand glass.
For vignetting caused by the condenser set to happen, either the coverage angle is too narrow—wrong condenser set for the format—or the distance from the condensers to the negative is too close.
I don’t know the design of the Kaiser enlarger. The Beseler 23C, CII, and CIII use a variable-position light source and condenser set mounted into a single unit that is raised or lowered relative to the negative so that the converging beam is concentrated to cover the diagonals of the negative. To aid in the placement, Beseler has included a format scale and indicator on the right side of the upper unit.
I have found that it can project a vignetted ring about the corners like the description in post #1, even when the indicator is positioned correctly. In the case of the 23C series enlargers the final position of the upper unit is best checked as follows:
1. With the lens installed, compose, and roughly focus the image of a negative.
2. Remove the negative and leave the carrier in position.
3. Carefully observe the projected light that falls upon an upside-down scrap sheet. The projected light should be of uniform intensity.
4. If any vignetting is seen, disregard the format indicator and adjust the position of the upper unit until the vignette disappears and the illumination is uniform, Replace the negative into the carrier, focus, and you’re ready to print.
https://cameramanuals.org/topcon/beseler_23cii-pr.pdf
http://www.jollinger.com/photo/cam-coll/manuals/enlargers/beseler/Beseler_23C_II.pdf
Regarding the Kaiser enlarger, it seems that either the wrong condenser set is installed, or it’s not properly positioned relative to the negative.