Let $\pi:Y\longrightarrow \mathbf{P}^1_{\mathbf{Z}}$ be a finite surjective flat morphism of schemes, where $Y$ is a normal integral flat projective 2-dimensional $\mathbf{Z}$-scheme, with branch locus $D$. Let us suppose that $\pi$ is tamely ramified.

**Question 1.** Does this mean that for every prime number $p$ such that some vertical component of $D$ maps to $p$ in $\textrm{Spec} \mathbf{Z}$ does not divide the degree of $\pi$?

By Abhyankar's Lemma, there exists a number field $K$ with ring of integers $O_K$ such that the branch locus $D\subset (B_{O_K})_{\textrm{hor}}$ of the morphism $\pi_{O_K}:Y_{O_K}\longrightarrow \mathbf{P}^1_{O_K}$ is horizontal.

By embedded resolution, there exists a projective birational morphism $f:X\longrightarrow \mathbf{P}^1_{O_K}$ such that $f^\ast D$ is a divisor with normal crossings.

**Question 2.** Since $D$ is horizontal, does it follow that $f^\ast D$ is horizontal. I thought so but wasn't completely sure.

**Question 3.** Does the (edit: normalization of the) fibre product $Y^\prime$ of $Y_{O_K}$ and $X$ over $\mathbf{P}^1_{O_K}$ give a morphism $Y^\prime\longrightarrow X$ with branch locus a horizontal normal crossings divisor? I would be surprised if the branch locus picked up vertical components...