  A decomposable strongly critical Galton-Watson branching process with $N$
types of particles labelled $1,2,...,N$ is considered in which a type~$i$
parent may produce individuals of types $j\geq i$ only. This model may be
viewed as a stochastic model for the sizes of a geographically structured
population occupying $N$ islands, the location of a particle being considered
as its type. The newborn particles of island $i\leq N-1$ either stay at the
same island or migrate, just after their birth to the islands $%
i+1,i+2,...,N$. Particles of island $N$ do not migrate. We investigate the
structure of the family tree for this process, the distributions of the birth
moment and the type of the most recent common ancestor of the individuals
existing in the population at a distant moment $n.$
