The box on the screen just shows you your paper size, anything outside the box will not be printed. If you want simple and low tech, "group" your blueprints and move them each time you print so that you end up with a bunch of sheets that when taped together will make your larger blueprint.
Artboards are treated differently depending on what version of Illustrator you haveand I'm guessing that if you see a blue box it's a pretty old version.
Artboards are treated differently depending on what version of Illustrator you haveand I'm guessing that if you see a blue box it's a pretty old version.