The basic technique is easy.
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first file is a quickie - look at feature statistics and you will see it took me five minutes from start to fiinish. So I am guseeing that this is not want you want because you could've pulled this one off simply with fillets and you would have figured that out for yourself. Instead of fillets I modeled a more flexible option so you could see another way of doing it. After posting that file I thought I would also post something less 'easy', and if you look at feature stats of 'more complicated Y branch', minus the time to debug this new web page, etc,etc., the modeling time was more like 20 minutes. When you vary from the obvious, lofts (or boundary or fill) require some art, In the case of 'more complicated Y branch' I needed to back off the split lines to give more space for the fill to do its business. I hope this helps, but I suspect that you still don't have your answer. I have been helping folks here for a very long time (I think I've just crested a decade) and know that, when it comes to these sorts of joints, the specifics really, really, really, really, really, really matter. The final solution will probably be similar to one I provided, but it might also need to include a Loft or Boundary ACROSS the gap to control the fills that are used to fill in the gap If you came to me with the exact diameters and orientations of your three cylinders and the exact 'character' of the joint you desire(does it bulge out, does it flow straight, etc) I could likely show you how to nail it. Good luck! Hope some of this helps! Ed