If you're explicitly setting the height of the parent, you can set the child's height to be 100% to achieve this effect. View on JSFiddle.
css
#parent {
background: #eee;
height: 200px;
}
div div {
background: #aaa;
height: 100%;
}
HTML
<div id="parent">
<div>lalala</div>
</div>
If you're not explicitly setting the height, you'll need to specify the question more. Divs are block level elements and want to take up an entire row to themselves. The code you posted will result in the child div and the text of the parent being on different rows. Because of that, it's hard to know what height you're looking for...maybe if the parent just had text? And then, what do we do with the div in relation to the text? Overlap it? Or push the div out the bottom of the parent?