  We expand the classical balayage of measures and subharmonic functions on a
system of rays $S$ with a common origin on the complex plane $\mathbb C$. This
allows for an arbitrary subharmonic function $v$ of finite order on $\mathbb C$
build $\delta$-subharmonic function on $\mathbb C$, harmonic outside $S$
coinciding with $v$ on $S$ outside the polar set, of the same order of growth
as $v$. We give applications to the relationship of the growth of an entire
function in $S$ with the distribution of its zeros.
