I think they keep em and you get an electronic print out but they keep the actual check..maybe im wrong or maybe each bank is doing it their own way but mine just gives you a photostat of all of your checks
My advice: Write down any questions you have, call your bank's toll free customer line, get the facts straight. Be sure to get the name of the telephone representative, don't hesitate to ask them to slow down in their explanations if you are jotting stuff down. Break yourself of the habit of floating checks immediately. What are you, the government??!
FReegards!