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What has become known as Stahl's Theorem in power-engineering circles hasbeen used to justify a convergence guarantee of the Holomorphic EmbeddingMethod (HEM) as it applies to the power-flow problem. In this, the second partof a two-part paper, we examine implications to numerical convergence of HEMand the numerical properties of a Pad\'e approximant algorithm. We show thateven if the convergence domain is identical to the function's domain, numericalconvergence of the sequence of Pad\'e approximants computed with finiteprecision is not guaranteed. We also show that the study of convergenceproperties of the Pad\'e approximant is the study of the location ofbranch-points of the function, which dictate branch-cut topology and capacityand, therefore, convergence rate. We show how poorly chosen embeddings canprevent numerical convergence.

Implications of Stahl's Theorems to Holomorphic Embedding Pt. 2: Numerical Convergence