CSS Dropdown Menu, Child Exceed Parent Width - css

Question

I'm trying to build a centrally-aligned dropdown menu, using HTML5 and CSS3. I could use jQuery to assist, if I must. This must work in IE8+. At the moment, my menu is centrally-aligned, and the drop-downs work, but the width of the dropped-down item (div) is the same width as the li above.
<div class="menu">
<ul class="level0">
<li class="level0">
<a href=" http://domain.com/">
<span>home</span>
</a>
<div class="sub">
<div class="sub-column">
<a href="http://domain.com/customer-service">
<span>Customer Service</span>
</a>
</div>
<div class="sub-column">
<a href="http://domain.com/privacy-policy">
<span>Privacy Policy</span>
</a>
</div>
</div>
</li>
<li class="level0">
<a href=" http://domain.com/about">
<span>About Us</span>
</a>
<div class="sub">
<div class="sub-column">
<div>
<p>Blah blah blah, some random text goes here.</p>
</div>
</div>
</div>
</li>
</ul>
</div>
And the CSS (tried to compact it for easy viewing).
.menu {
clear:both; display:block; max-width:100%; margin:0 auto; padding:0;
border:1px solid #ddd; border-bottom:7px solid #323131; text-align:center;
}
.menu ul {
display:block; max-width:100%; height:3.2em; margin:0 auto;
padding:0; list-style-type:none; text-align:center;
}
.menu ul li {display:inline-block; margin:0; padding:0; height:3.2em;
line-height:3.2em; position:relative;
}
.menu ul li > div {display:none; visibility:hidden; position:absolute;
background:#f60; z-index:999; transition:display 0.25s ease;
}
.menu ul li:hover > div {display:inline-block; visibility:visible;
max-width:100%;
}
.menu ul li a {display:block; margin:0; padding:0 2em; font-size:90%;
font-weight:700; text-transform:uppercase; transition:background-color 0.25s ease;
}
.menu ul li a:hover {background-color:#e4e4e4; color:#323131;}
.menu ul li.switcher {display:none;}
How can I get the width of the first line div (.menu ul li > div) to adopt the width of the grandparent element (.menu)? Or at least stretch to fit the contents in using max-width?
Any help is appreciated. Thanks.
~ edit ~
Here's the fiddle: http://jsfiddle.net/Xp6yG/

Answer 1

I think I understand your issue correctly, try the following:
fiddle demo
CSS:
.sub {left:0px;}

Answer 2

As well as using James suggestion of making the .menu position: relative I think you will also need to remove the position: relative on .menu ul li

Answer 3

Thanks to some helpful suggestions, this is as close to working as I've got it: http://jsfiddle.net/Xp6yG/3/.
I changed the display on .menu ul li:hover > div to display:table; and added whitespace:nowrap; and right:50%; to the .menu ul li > div element.
The dropdown appears where I want it and stretches to fit the containing element(s). Thanks very much all!