There is NO way to exactly fill a screen vertically that works on all browsers, screen resolutions, and viewport sizes.
- It's impossible to make a page that fits perfectly in the vertical direction on all monitors.
- It is impossible to place anything against the bottom edge of the screen.
The Internet is not designed to work that way. It is designed to expand pages downward as much as is necessary to fit the entire content served. Screen height and the bottom edge of the screen are undefined in Internet protocols.
You can choose among these possibilities:
1. Design your page for one screen resolution, and accept the fact that people with other screen resolutions are going to see either scroll bars or a smaller page in the upper left corner.
2. Design your page for the lowest resolution, and let the remainder of the screen be blank if a higher resolution monitor displays it.
3. Design your page to fit against the top of the screen, and expand to fit the width (which does work). Use a repeating background image to fill the rest of the screen downward.
4. You could try to wrestle with JavaScript functions intended to find the screen height. But they are not standardized across browsers, and are totally undefined on many browsers.
5. You could create an image containing the entire page, and then choose a display that fits the image to the window horizontally. It will then approximately fit vertically. But it won't work right on the new widescreen monitors. And you can't have any links on this page.