Kevin Costner's divorce was as ugly as they come -- and much of it had to do with claims of infidelity on both sides ... something denied by all sides and featured in a new 'TMZ Investigates.'

The A-lister's split from his wife, Christine Baumgartner, kickstarted with unfounded rumors of KC impregnating someone on the set of "Yellowstone"  -- something we dive into in detail in a new documentary airing Monday on FOX, 'Kevin Costner's Divorce War.'

Now, when it comes to CB herself -- there were rumblings of alleged cheating as well ... on two different fronts, actually. There was a guy who was staying in their guest house -- whom she was alleged to have slept with -- he shut that down, saying it never happened.

There was also Josh Connor ... a friend of Kevin and Christine who -- as soon as they were in the midst of divorce -- started to hang out a lot with Christine on vacations. Again, sources connected to both of them say there was absolutely nothing romantic going on before or during the divorce.