Let $B=B(0,1)$ be the open unit disc in $\mathbf C$. Let $X\to B$ be a smooth projective morphism of complex manifolds with $X$ connected.
What can we say about $X$?
For instance, if $X\to B$ is of relative dimension zero, we have that $X\cong B$.
Does a similar type of "triviality" hold in relative dimension $>0$? That is, do we have that $X \cong B\times V$ for some manifold $V$?