The border continuations in Strips and Curves are generally NOT appliquéd, at least not the circles and strata ones. They are pieced, just like the rest of the quilt. If you have the first book, look at the corner of Ripples on page 56 in the discussion about borders. There is a seam line where the side border meets the bottom border through the middle of the strata strips. It just takes planning and, if the circle passes under the inner border, you have to remember to reduce it's size by the width of that border, otherwise it becomes an oval.