What i believe is not exactly the multiverse theory.
It's more likely "adaptative time" or something like that.
If you were able to travel in time, the sequence I imagine is something like this:
You born in 1960 (for example)
You hate your father in 1985, and decide to ERASE him from the history, so you go back in time to 1950.
You kill your father in 1950. Then, if you continue living from here, you'll be a person that nobody knows where you came from. Only you know you borned on 1960 (or should born 10 years later, hehe), but obviously, you'll never born in 1960 from here (due to the change you have just made).
Now, imagine you regret yourself for killing your father, and go back to 1985 trying to stop yourself going to the past. The 1985 you'll go is no more the one you started the trip. It's the 1985 since you killed your father, so nobody knows you have traveled in time and killed your father, in fact, nobody knows you. You'll not find yourself on 1985, because you traveled to 1960 and changed things.
The only way you have to save your father is going to the past, to some moment before you killed him (1945 for example). Then, doing nothing more, you just jump to 1985, this 1985 would be the same as if you have not travelled, because in fact, it's like if you have traveled to 1945 and then to 1985, touching nothing.
So, you can make all the strange things you want, and visit all the possible futures from this actions (trying not to be killed in the process, hehe). To restore the time-line you want, you'll have to go to a moment before you did the actions you don't desire, and then go back to a moment after you started the time travel. (do you know how the tool HYSTORY works in PHOTOSHOP?... something like this)
Every jump to the past makes this past convert into present, and erase the rest of the future that you know it happened from that moment. It's time that have not happened (and will not happen) to anybody else.
If you travel to the future, it will be the same as if you just have disappeared for that years.
Another interesting thing is that there can only be one time-traveller, the time traveller that goes more into the past makes the rest of the time travellers depend on his actions. Maybe this deeper-past-time-traveller will change the time in a way that the other possible time travellers will not travel. The time-travel possibility depends of this deeper-past-time-traveller.
To me, It's similar to multiverse theory, but with a collapsing of the multiverses into only one time-line on every time travel.