  This paper is concerned with the existence and uniqueness of transition
fronts of a general reaction-diffusion-advection equation in domains with
multiple branches. In this paper, every branch in the domain is not necessary
to be straight and we use the notions of almost-planar fronts to generalize the
standard planar fronts. Under some assumptions of existence and uniqueness of
almost-planar fronts with positive propagating speeds in extended branches, we
prove the existence of entire solutions emanating from some almost-planar
fronts in some branches. Then, we get that these entire solutions converge to
almost-planar fronts in some of the rest branches as time increases if no
blocking occurs in these branches. Finally, provided by the complete
propagation of every front-like solution emanating from one almost-planar front
in every branch, we prove that there is only one type of transition fronts,
that is, the entire solutions emanating from some almost-planar fronts in some
branches and converging to almost-planar fronts in the rest branches.
