  Conditioning a multitype Galton-Watson process to stay alive into the
indefinite future leads to what is known as its associated $Q$-process. We show
that the same holds true if the process is conditioned to reach a positive
threshold or a non-absorbing state. We also demonstrate that the stationary
measure of the $Q$-process, obtained by construction as two successive limits
(first by delaying the extinction in the original process and next by
considering the long-time behavior of the obtained $Q$-process), is as a matter
of fact a double limit. Finally, we prove that conditioning a multitype
branching process on having an infinite total progeny leads to a process
presenting the features of a $Q$-process. It does not however coincide with the
original associated $Q$-process, except in the critical regime.
