Are the rotation axis of bodies randomly determined?
Well…yes and no. The rotation axis of a particular body is probably determined by the types of gravitational encounters it has had in its recent past. Example, the planets in our solar system passed through a period of intense asteroidal bombardment with progressively larger bodies as the solar system aged. The last few of these large bombardments may have been with objects the size of small moons, and these would have tilted the axis of the planetary rotation. Even galaxies that rotate have axis that are affected by tidal collisions with nearby galaxies. So, for any specific object, the rotation axis is determined by the detailed geometry of the interaction, and is not random. For a collection of objects, such as the stars in the Milk Way, there might be a weak tendency for the rotation axis to be perpendicular to the plane of the Milky Way, but no one really knows. Stellar orientations seem to be more influenced by local phenomena within the interstellar cloud that produced them, t