Recently I came across a great article which presents a pro/cons and comparison of the various techniques, then presents a different and more robust branch joint solution. Basically the key realisation is that the problem can be boiled down to 2 main areas convex hull construction and subdivision loop method.
The following proof of concept demonstrates a trivial case for performing branching joints
In order to test the join process, firstly copying Tubes of various size and resolution to Tetrahedron points resulting in the above geometry
The tubes are Mesh geometry not polygons, this allows to carve off the end edge loops
Number simply illustrate that each has different point counts
Tetrahedralize SOP is used to generate a convex hull geometry
The convex hull creates geometry superfluous to need, which can be rectified by taking the dot product of the primitive normals of the convex hull source geometry and convex hull itself
Geometry can be removed where it satisfies certain criteria produced by the dot product
Merging tubes with convex hull, perform cleaning with PolyDoctor SOP correct winding of polygons and creating vertex normals
Finally a Subdivision SOP using the method of OpenSubDiv Loop generates the best results, others cause rippling effects
