When the person or object goes back that split second, they can create a paradox, but the universe resolves that paradox not by creating alternate timelines, but by resetting. Whatever happened in the split second after the time-traveler arrived stops existing, as though it had never happened. However, the time-traveler does not get wiped out. Anything sent back in time still exists.
Result: You can make as many of anything as you want--people, objects, etc. Also, because the Earth is moving during that split second, the extra objects can essentially teleport, though only a matter of fifty feet initially. So when you invent time travel you also create a matter duplicator where you actually have to jump through quite a few hoops to keep from going into an endless loop of creating more and more of whatever object you send back. Want more Steven Hawkings? You can make as many as you want. Want more dynamite? Same thing.
This is a packaged as a thriller rather than science fiction, but it’s quite good as science fiction, with a very thoughtful and unique approach to time travel.
Then we have Return to Sender by Fred Holmes. Basically a neo-Confederate figures out a way to travel back in time. He decides to use it to save the Confederacy by keeping Stonewall Jackson from dying.
Mild Spoilers ahead.
The plot succeeds, and we end up with a Confederate States of America. That turns out not to be a good idea. The resulting divided US proves to be easy prey to predatory neighbors.
The book pauses to give us a detailed timeline of how badly things went wrong. Some of it is reasonably plausible but much of it isn’t at all plausible, at least not to me. That’s not the main problem with this novel though. The big problem is that the author really hasn’t thought through the personal implications of making a big change over 150 years in the past. People change the past and don’t simply disappear, which is prerty much inevitably how things would happen.
At a panel I watched a while back, Eric Flint estimated that nobody born more than three years after a major timeline change would still be born. That may be a little pessimistic, but I would agree that nobody born ten years after a Point Of Divergence on their continent and nobody in the world after maybe the early 1800s would be born in the alternate timeline. Given the odds against a particular sperm fertilizing an egg, mommy and daddy have to do the nasty within split seconds of when they did so historically and do in the same position at the same precise angle. If they’re even a little less of more enthusiastic, somebody with your name may be born on your birthday, but they would be your brother or sister, if you were ever born, which you won’t be, not you.
The implausibility of the time travel and the resulting timeline aside, this isn’t an altogether bad book. The history is reasonably well researched. The writing isn't perfect, but it is good enough to keep me reading until the end, which isn’t a given by any means.