It all depends on how time travel works. There are a couple lines of thought that say paradoxes are impossible. If you go back in time and do something, you were meant to, and that's how it was supposed to roll out anyways. Say you went back in time to kill Hitler. You show up at the Hitler residence, walk in and shoot a young Adolph Hitler. What you have done is allowed the family to adopt his friend, unknown to the rest of the world, as their own, and you shooting his buddy made him evil, and he took on his name, becoming the Hitler from history. (its a bad example but all I could think of) Another is that timelines can't be altered, and really you just travel between possibilities. So, you go back and shoot Hitler. In your originating timeline, you just left to parts unknown, WWII happened just as it did etc.. But in your new timeline you became a catalyst for a new history. The two exist separately.