On the classification of points of the unit circle for subharmonic functions of class $\mathfrak{A}^*$

In this article, we consider a class $\mathfrak{A}^*$ consisting of functions, subharmonic in the unit disk and such that their compositions with some families of linear fractional automorphisms of the disk form normal families. We prove a theorem which states that for any function of class $\mathfrak{A}^*$ the set of points of the unit circle can be represented as a union of Fatou points, generalized point Plesner, and a set of zero measure.