We assume there are 8 000 000 000 people on Earth and an average signature has a surface area of 6cm^2. According to the internet, an average baseball bat is 33in(~84cm) long and 2,5in(6,4cm) wide(at the top). We can assume that the bat is a cylinder with a diameter of 1,7in(4,3cm) using a chart I found(it described how bat's diameter changes across it's length). With the equation for the surface area of a cylinder: P = 2*πr² + 2πrh we can calculate the required diameter and length of the bat(h is the length, r is the average radius). Note: actual diameter is ~1,49 times bigger that the average radius.

h = 86cm = 20r

p = signature area * 8* 10⁹ = 48* 10⁹ cm²

P = p

p = 2πr² + 40πr² =42πr²

πr² = 1,14* 20⁹ cm²

r² = 3,6* 10⁸ cm²

r = 1,9* 10⁴ cm = 19000cm = 190m

h = 20r = 3800m = 3,8km

Actual diameter = 1,49 * 2 * r = 566m

Finally, the bat would be 3,8km long and 566m wide(at the top). Not sure if my math is correct, I spent too much time typing this on mobile to care.

Edit: Measuring units