They can from either a star or a nested hierarchy depending on your working assumptions. The pattern is made by humans. In the case of the paper you cited a single starting point is assumed. The null was where divergence did not change and that is an unrealistic common design model.
You do not know at this point that they converge on a single ancestor. The single ancestor is inferred however it could as easily be multiple starting points of the same sequence and the data would not differentiate that;
The extreme level of preservation should make you conducer if the sequence is the product of evolutionary processes.
Where did these highly preserved proteins come from? The sequences live in almost infinite mathematical space(infinite possible arrangements) yet they get stuck in a very narrow band of amino acid arrangements. How is the diversity of proteins produced given this observation?