if the average signature takes up an area of 20cm² (including necessary padding), and if every person of the 8 billion alive has indeed signed that bat, then the total space taken for the signatures would be 160 billion cm²--or 16km², which is about as big as most airports.
the ratio of length of a baseball bat to its average diameter is 42": 2". since height (h)=42x the radius (r), the equation for the surface area of a baseball bat simplifies to 42πr³.
so if our baseball bat holds all 8bn signatures on its 160bn cm² surface, the radius of such a bat would be ~1066cms, or 11 meters. and its length would be 447 meters or about six 747s stacked nose-to-tail human-centipede style.
(yes, this has been a productive saturday morning, indeed.)
(edit: minor corrections.)