I am using Windows, and I have two monitors.
Some applications will always start on my primary monitor, no matter where they were when I closed them.
Ot
Get UltraMon. Quickly.
http://realtimesoft.com/ultramon/
It doesn't let you specify what monitor an app starts on, but it lets you move an app to the another monitor, and keep its aspect ratio intact, with one mouse click. It is a very handy utility.
Most programs will start where you last left them. So if you have two monitors at work, but only one at home, it's possible to start you laptop at home and not see the apps running on the other monitor (which now isn't there). UltrMon also lets you move those orphan apps back to the main screen quickly and easily.