The answer is A: the center of gravity.
This rests on the assumption that the ball is thrown in real space where gravity is a given phenomena that exists.
It is difficult to theorise about the way the ball would spin, if indeed it would spin at all, if it were weightless. What could be said is that the ball would appear to be moving away, from the point of view of the person throwing it. Equally, the person throwing it would appear to be moving away from the ball, to any observer that might be sharing the balls perspective.
Deep in space, in places far from massive bodies (with gravitational pull), near weightlessness might be experienced. Total weightlessness however may be just a concept.
When a ball is thrown on Earth (Earth is a massive object in space, from our point of view at least), it has been found that the flight of the ball follows a path such that its center of gravity runs along a parabola, the parabola curving down to the ground. This is a smooth process - balls in flight never 'judder', unless they be buffeted by the wind or bump into other objects - so that it must be that the ball is rotating smoothly about the center of it that is following the smooth parabolic path. Which is to say, it must be rotating somehow smoothly about its center of gravity.
The center of gravity of an object can be located by hanging the object from a string, known as creating a 'plumb line'. Following straight down from where the string is attached to the ground (the direction gravity pulls to), we know that (for regular objects, specifically with no holes) the center of gravity is somewhere on that line. The spot is then more precisely located by lowering the object directly to the ground. If it falls over when the string is removed, the center of gravity is more than half way up. Experimenting with placing the object in various ways upon the ground and seeing when it does and doesn't fall or teeter allows closer and closer location of the balance point, ie the center of gravity.
For a regular spherical ball with even density (unbiased weight) the center of gravity is in the very center of the ball whichever way it is placed on the ground. Only if the ground is sloped, or there is insufficient friction somehow to hold the ball in place, will it move.
Answer A: the ball spins naturally about its center of gravity. [For balls, the center of gravity is simply the center of the ball].