We have several styles of borders that you can choose for your t-shirt quilt. First a few definitions so we all know what we are talking about.
Binding is the finishing method that goes around the outside edge of the quilt. It covers up the raw edges of fabrics and makes a nice finish. This fabric is usually the same fabric as the outer border or backing of the quilt.
Borders are part of the quilt top and effect the finished size of the quilt. There can be one or more of these, each adding to the interest of your quilt
Read more about the difference between borders and binding. Many quilt/(blanket) makers just sew the shirts together, and finish it in one of several methods. The CHEAP blanket guys, just make the top (see Terms), sew it pillowcase style, then top-stitch around the outside edge. (Note: that is finishing the edge, but is not binding)