  We prove several results concerning the relative position of points in the
postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker
domain or the successive iterates of a wandering component. For Baker domains
we answer a question of Mihaljevi\'c-Brandt and Rempe-Gillen. For wandering
domains we show that if the iterates $U_n$ of such a domain have uniformly
bounded diameter, then there exists a sequence of postsingular values $p_n$
such that ${\rm dist}(p_n,\partial U_n)\to 0$ as $n\to \infty$. We also prove
that if $U_n \cap P(f)=\emptyset$ and the postsingular set of $f$ lies at a
positive distance from the Julia set (in $\mathbb C$) then any sequence of
iterates of wandering domains must contain arbitrarily large disks. This allows
to exclude the existence of wandering domains for some meromorphic maps with
infinitely many poles and unbounded set of singular values.
