You can choose!
Obviously if you stretch it across both the crosshair will be on the divide and that will look strange and not really be playable.
The best thing to do (and what it sounds like you're asking if you can do) is set it to run on one screen maximised, while continuing tasks on your other screen.
But say as your using your gun playing. If you put the mouse too far on the right wont it go into your other programs. I want to stay in the one screen.
I think you just ALT+TAB like normal and it takes the mouse focus to the other screen.
I've never used dual screens myself, just going off what I've heard