Balayage of measures and subharmonic functions to a system of rays. II. Balayages of finite genus and growth regularity on a single ray

The classical balayages of measures and subharmonic functions are extended to a system of rays $ S$ with common origin on the complex plane $ \mathbb{C}$. For an arbitrary subharmonic function $ v$ of finite order on $ \mathbb{C}$, this allows one to build a $ \delta $-subharmonic function on $ \mathbb{C}$ that is harmonic outside of $ S$, coincides with $ v$ on $ S$ outside of a polar set, and has the same growth order as $ v$. Applications are given to the investigation of the relationship between the growth of an entire function on $ S$ and the distribution of its zeros. In the present second part of the project, the results and preliminaries of its first part are used essentially.