  We answer an open question concerning the boundedness of canonical fiber
spaces in high dimensions and prove the following: for any set of integers
$n\geq 3$, $0<d<n$ and $N>0$, there exists a nonsingular projective $n$-fold
$X$ of general type so that $X$ is canonically fibred by $d$-dimensional
varieties $F$ with $p_g(F)\geq N$. This disproves the desired boundedness
parallel to Beauville's boundedness theorem in the surface case.
