All-height version of Manin's conjecture over global function fields

Let $\pi:\mathcal X\to B$ be a good Fano fibration, let $\lambda$ be an intersection profile, let $M_{\alpha}$ be the unique Manin component for sufficiently large $\ell_{\lambda}(\alpha)$, and let $M_{\alpha}^{\circ}$ be its complement of the properly constructible exceptional locus. All-height version of Manin's conjecture. There exist constants $c(\mathcal X,\lambda)\geq0$ and $\delta>0$ such that

$$\#M_{\alpha}^{\circ}(k)=c(\mathcal X,\lambda)q^{-K_{\mathcal X/B}.\alpha+n(1-g(B))}+O\left(q^{-K_{\mathcal X/B}.\alpha-\delta\ell_{\lambda}(\alpha)}\right)$$

as $\ell_{\lambda}(\alpha)\to\infty$, where $n=\dim\mathcal X_{\eta}$. This is compared in the source with analogous proposals of Bourqui and Peyre; no resolution status is supplied.