If you are working to NAVSEA TP278 you need to refer to MIL-STD-22D for the various joint details that are acceptable per TP278. Then you have to review the welding requirements to establish which weld classification you fall into (it should be on the drawing and if it isn't ask why it isn't). Once you know the weld classification you refer to TP278 Table VII to see if the joint detail taken from MIL-STD-22 is listed for that class. If the joint detail isn't listed as an approved joint, you have to qualify the WPS using the proposed joint detail and have it approved by the activity (the particular ship yard you are working with) before going into production. If the joint detail is listed, refer back to MIL-STD-22D to see the details of the specific joint detail specified by the drawings. Don't forget to review the inspection requirements listed in NAVSEA TP278 Table IX to ensure no critical inspections are overlooked.

In rereading your post I noticed the branch connection you are concerned with is a CJP accessed from one side. Please note that for practical purposes, NAVSEA TP278 does not permit single sided CJP welded joints made without backing except in a vew few cases.

As for ASME, you have to know which piping code you are working to. Each piping code, i.e., B31.1, B31.3, etc., has unique welding requirements for branch fittings. The specific requirements should be addressed in the appropriate WPS or other working document. It should not be left to the welder or the inspector to figure out what requirements apply. There are a number of reasons why the welder or the inspector is not expected to determine what piping code applies. The number one reason that comes to mind is that neither the welder nor the inspector knows how the system was designed. While they can use the "SWAG' method of determining the welding requirements, it is the owner's legal obligation to determine what piping code is applicable. The engineer, working for the owner, is responsible to develop the project specifications which should list the appropriate piping code. As mentioned, the welding requirements vary from one piping code to the next, so there is no one correct answer to your question. Just one point of information, if you take the time to look in the appropriate piping code, the size of the fillet weld is often listed as the minimum throat dimension, not the leg size. Multiply the throat by 1.414 to get the equivalent leg dimension. A well written WPS should address many of your concerns.

I like Joe's suggestion, use a Tee if you are working to an ASME piping code.

Best regards - Al