It's really important to read the instructions that come with the batting. Cotton battings like Warm & Natural, Hobbes Heirloom cotton Blend batting, etc. have instructions for pre-treating the batt to preshrink. I have a top loading machine and soak my Hobbes batting in cool water, spin it dry, then lay it on a spare bed to air dry. I do not aggitate the batt in the wash cycle, nor do I dry it in the dryer before I assemble my quilt for quilting.
Some cotton battings do not recommend pretreating, so be careful. Even without pretreating, the battings will shrink about 5% so you won't have a situation where a full size quilt shrinks dramatically to a twin.
Hope this helps.
kim