On the branch points of mappings with the unbounded coefficient of quasiconformality

We study relations between the quantity characterizing the distortion of families of curves under a given mapping and the structure of the branch point set of this mapping. For $n\ge3$ we establish that the image of the branch point set of an open discrete mapping with an isolated essential singularity is an unbounded set in $\mathbb R^n$ provided that the mapping satisfies certain geometric conditions controlling the distortion of concentric annuli centered at this point.