"the maximal singular fibers" means the number of components are maximal. Alex: could you please give the description (or reference) of fibration on $K3$ with $\tilde{D_{16}}$ singular fiber. Thanks

I meant ${I^{*}}_{14}$.

Sometimes the same singularity is denoted as ${I^{*}}_{19}$. Yes, such fibration exists according to some literature. It has the maximal singular fibers.

Dear Will, Thanks for your answer. Why your argument doesn't apply when $S$ is simply connected? I did not understand the statement "then you only need to note how the special fibers are quadratically twisted, which is also finite information"?