  Under natural assumptions, a Feller type diffusion approximation is derived
for critical, irreducible multi-type continuous state and continuous time
branching processes with immigration. Namely, it is proved that a sequence of
appropriately scaled random step functions formed from a critical, irreducible
multi-type continuous state and continuous time branching process with
immigration converges weakly towards a squared Bessel process supported by a
ray determined by the Perron vector of a matrix related to the branching
mechanism of the branching process in question.
