My question is if there is a way, without using JavaScript, to cause child divs to extend to the borders of their parent, without exceeding those borders, when you cannot kn
For width it's easy, simply remove the width: 100% rule. By default, the div will stretch to fit the parent container.
Height is not quite so simple. You could do something like the equal height column trick.
html, body {width:100%;height:100%;margin:0;padding:0;}
.border {border:1px solid black;}
.margin { margin:5px;}
#one {width:500px;height:300px; overflow: hidden;}
#two {height:50px;}
#three {width:100px; padding-bottom: 30000px; margin-bottom: -30000px;}