It can't exist in 3 branches. The Downfall Timeline is essentially a 'what if' scenario which comes into existence when Link falls to Ganon in the final battle, therefore Link is never sent back by Zelda and so the 2 splits never occur. By contrast though, the Adult and Child Timelines are...
Part of Breath of the Wild's marketing was for the player to be able to choose their own path. This could be carried over into its timeline placement. That is, if one player feels it's the DT and another think it's the AT- neither are wrong. The references and stuff aren't really that specific...