Assume we are given a Brauer class $\xi\in Br(k(\mathbb{P}^n))$ ramified at some divisor $D\subset \mathbb{P}^n$, here $k=\mathbb{C}$.

If $f: \mathbb{P}^n\mathrel{-\,}\rightarrow \mathbb{P}^n$ is a birational morphism, what can we say about the ramification of $f^{*}(\xi)\in Br(k(\mathbb{P}^n))$?

Is this still $D$ or can it be smaller, bigger or totally different from $D$? Is it birational to $D$? Do we have any control over it?

Maybe one can use the Weak Factorization Theorem, which states that $f$ can be written as a sequence of blow-ups and blow-downs with smooth centers. So one must just understand what happens to the ramification under smooth blow-ups or smooth blow-downs. For example if we blow up a point, can(must ?) the exceptional divisor be part of the ramification divisor? Or can one of the blow-downs reduces part of $D$ to a point? Is everything is possible here?

Is this known or written down somewhere in the literature?