NURBS surface from branching curves? I'm looking for a way to do something very similar to the technique using the skin modifier, but with NURBS. In other words, I'm looking for a way to do something similar to a convex hull, but not necessarily convex. I want a tree-like meshing with custom branch morphing.

Example with skin modifier:


With surfaces, the make segment command f doesn't allow to do branching.

Extruding a nurbs curve only works with uniform extrusion (unless I'm mistaken), meaning you cannot morph from, say, a circle to an oval. You can only uniformely reduce the size of the extrusion shape.

Python code is welcome as an answer.

Initial curves describing the volume: 

Desired meshing from NURBS: 
 
Make segment unwanted result:
Blender is not known or marketed for its NURBS support, it is primarily a polygon modelling tool. While we have great modifiers like the Skin Modifier you mentioned, we don't have anything out of the box that would produce comparable NURBS surfaces.

A scripted solution also seems a bit beyond what is convenient to do in Blender, the API has limited support for generating arbitrary patch shapes that would be needed to do your Question justice.

I'd like to be proven wrong someday, or today, but for now I'd like to offer this as an interim answer and not just a cheeky comment. There are better tools for generating NURBS, consider freeCAD or any of the other free CAD/NURBS alternatives.