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.
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Do not hold me to this but I am pretty sure it depends on the application it self. I know many always open on the main monitor, some will reopen to the same monitor they were previously run in, and some you can set. I know for example I have shortcuts to open command windows to particular directories, and each has an option in their properties to the location to open the window in. While Outlook just remembers and opens in the last screen it was open in. Then other apps open in what ever window the current focus is in.
So I am not sure there is a way to tell every program where to open. Hope that helps some.