If the two cats see each other at the same time, either they will both try to out-wait the other, or one or both will turn around and return the way they came. They will go through this ritual of avoidance even if one cat has already established itself as dominant over the other. Cats do not use their dominant or subordinate rank to control each other. A dominant cat will allow a subordinate cat to pass first on the pathway. A dominant cat will not take food away from a subordinate cat.
Cats seem to prefer non-confrontation.
If a confrontation does occur, it is usually a noisy ritual of aggressive displays, rather than actual tooth and nail combat. Part 1 dealt with the importance of scent, territory and early socialization. Before bringing home another cat, it is best to review these issues. If either cat has not been adequately socialized, the chances are high that they will not accept one another. If you are not sure how much socialization your cat received as a kitten, observe her behavior and temperament right now.