Since there is no ‘up’ or ‘down’ in space, the alignment is purely random. The ‘axis’ is simply from whatever point of space you view it...............
I have a doubt that the orientation will be purely random.
Certainly, planets revolving around a star generally rotate around poles that are roughly perpendicular to the plane of their orbit. So the polar alignment of planets bears some relationship to the sun they orbit.
Stars too bear a relationship to the supermassive black hole at the center of a galaxy. Stars orbit in a Galaxy. So stars too bear a spacial relationship to the galactic center.
Are there any hypotheses that seek to predict the orientation of the poles of a black hole, i.e. the gamma ray jets at either end, that corresponds to its spacial relationship to the the galactic center, or for that matter any other celestial object?