What happens with relics when characters are replaced? The Comprehensive Rule Book doesnt mention relics. Other types of objects are left in the square last occupied.

It actually depends on the situation. Standard objects simply drop to the map, as does any Equipment that says "Drop" instead of "KO." As for Relics, going back to the 2014 Players Guide (the last time they were officially ruled on), the rules did specify that they simply drop the map when the characters using them are defeated.

Right but if the character was being replaced and not KO'ed, I am wondering if the relic would stay on the old characters card.

For Relics, I can't find anything that would prevent it from simply staying with the replaced character on the Sideline.

The Comprehensive Rules says this about Resources:

But, obviously, Relics are not Resources. Looks like, in the modern world, once you have a Relic you can't lose it unless you are KO'd or some other effect gets rid of it.