There are places online where you can find out how much a specific batting shrinks. Sometimes this is printed on the packaging. A lot of cotton batting shrinks a maximum of 3%; however, a specific cotton batting could shrink considerably more or considerably less than this. There are many different ways even just cotton battings are manufactured, it's really impossible to give a standard for cotton.
Hobbs wool batting shrinkage is posted online -- somewhere between 1% and 3%, if memory serves me correctly. It can be machine washed and machine dried without excessive shrinkage.
Much depends not only on fiber content of the batting, but also on how the batting was manufactured (traditional, needlepunched, needlepunched through scrim) and also on the specific manufacturer.
One batting that does not shrink or change shape at all is 100% polyester batting, I think.
Oh, yes, and the amount of quilting affects amount of shrinkage also. Harriet Hargrave showed us a quilt she had made out of un-prewashed flannel (which has a reputation of shrinking badly). It was closely quilted by machine, and she measured it before and after it was machine washed and machine dried; very little shrinkage.