jte,
Actually each manufacturer may design their own, but they have to work within established tolerances. In your example of a tee, for instance, in the case of a butt-welded tee ASME B16.9 has a wall thickness tolerance of not less than 87.5% of nominal thickness, which should be adequate for reinforcement calculations, so you know if you've got a 8" Schedule 80 tee you've got a minimum wall thickness at any given position of 0.4375".
Have to admit I never really thought of it much since I've only worked on branch connections on pipe runs, but it got me looking, here's what I've found, using a butt-weld B16.9 elbow on B31.3 piping as an example. First off, article 1.3 of B16.9 states "Fabricated laterals and other fittings employing circumferential or intersection welds are considered pipe fabrication, and are not within the scope of this Standard". That says to me, once we add one of those elbolets to our butt-weld elbow, if I consider that an intersection weld, that elbow is no longer under B16.9 design.
If that belief is correct, then our butt-weld elbow/elbolet fitting is no longer a listed component as defined by B31.3 paragraph 303, and a design calculation is required per section 304. That's where I lose track of things, as strictly speaking nothing in 304 really seems to apply to this particular example.