Let $X$ be a regular arithmetic surface over a number field $k$, let $P \in X(\bar{k})$ be an algebraic point. Let $K=k(P)$, the defining field of the point $P$. Let $B'$ be the arithmetic curve corresponding to $\text{Spec }\mathcal{O}_K$. So then we can view $\pi: X \to B'$ as a regular model of $X_{\eta}$, where $\eta$ is the generic point of $B'$, and also view $P$ as a point on $X_{\eta}$.
Let $E_P$ be the closure of $P$ in $X$, which is known as the horizontal divisor corresponding to $P$ with $\pi|E_P$ is surjective. $E_P$ also comes together with a section $i : B' \to E_P$ (wrt the fiberation $\pi$).
One claim: this $i$ is actually a normalization (or B' is a normalization of $E_P$). I am not sure how to see it. I guess the $i: B' \to E_P$ is something like sending $b \in B'$ to $E_P \cap X_b$, where $X_b$ is the fiber. Other than that, I have no clue (or maybe that is also wrong).