Staying with the book analogy, let us consider three kinds of people.
A non-time traveler is a single world line with memories accumulating from left to right across one page of the book.
A time traveler who remains in a single timeline is several world lines of different lengths. Within each world line, his memories accumulate from left to right. However, in his subjective experience, any given world line might exist later than one to its right, i.e., if he has traveled into the past.
A time traveler who, having traveled into the past, returns futureward but arrives in an alternative timeline - he comprises at least one world line on page x of the book and at least one world line on page x+1. Having arrived on page x+1, he might think that page x has ceased to exist or even that it has never existed. However, from the perspective of those who remained om page x, he has disappeared. He has departed on a time journey but has not re-appeared at any other point along their timeline.