It depends on the friction of the contact. With a frictionless plane the top would precess around its center of gravity and the contact point will prescribe a circle.
Add friction, and the friction force translates the center of gravity the same way tire traction translates a car. Here you have the cases of a) pure rolling, or b) rolling with slipping.
With pure rolling the motion is similar to a spinning coin rolling on its edge, or a spinning glass which precesses in a circle smaller than the contact ball radius.
With slipping there isn't enough force for such a tight circle, so the precession yields wide circles that become progressively smaller and smaller.