Huynh–Wood complete-bipartite-minor-free counting conjecture

Let $s$ and $t$ be positive integers with $s\leq t$, and let $\mathcal G$ be the class of graphs containing no $K_{s,t}$ minor. Let $H$ be a graph containing no $K_{s,t}$ minor. For a graph $H$, let $\operatorname{flap}_{s-1}(H)$ denote the maximum size of an independent collection of separations of $H$ of order at most $s-1$. Huynh–Wood's conjecture.

$$\operatorname{ex}(H,\mathcal G,n)=\Theta\left(n^{\operatorname{flap}_{s-1}(H)}\right).$$

The conjecture was proposed by Huynh and Wood as a potential answer to a question of Eppstein. The supplied text does not give evidence that it has been solved or refuted.