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Byakuran's power is to communicate with other Byakurans in the parallel worlds. He can not travel to another parallel world.
If you have read up to the current chapters then you will know about Yamamoto. If not then I will not say what exactly happens with him.
The way I see it the way that current day Byakuran could do something with his powers is if he had the memories of his future self or someone helped him to reawaken his powers.
i think byakuran will prove to be an amazing asset to vongola family in the following events given he also received those future memories and as far as i'm concerned i think he's the kind of guy that knows how to accept defeat with a smile on his face and move on just like we saw in the future arc.... he helped yamamoto 'cause he felt he had to and in a way i guess he might have understood that his actions were not right ...i might even say that he will help the vongola family from the shadows from now on but i'm still not 100% sure about his real intentions yet
i all was like byakuran. I think that he has given up on trying to take over the world's and has face the fake that tuna is stroger then him. He is trying to say sorry for all the thing that he did by helping them out. I also think that he is going to tell them a way to get ever one that lost there fight as now they all know what damon had done to them.