We study asymptotic behavior of positive ground state solutions of the nonlinear Choquard equation with a Sobolev critical attractive local perturbation where \(N\ge 3\) is an integer, \(p\in \big (\frac{N+\alpha }{N}, \frac{N+\alpha }{N-2}\big )\) , \(2^*=\frac{2N}{N-2}\) is the Sobolev critical exponent, \(I_\alpha \) is the Riesz potential of order \(\alpha \in (0,N)\) and \(\varepsilon >0\) is a parameter. We show that as \(\varepsilon \rightarrow \infty \) , after suitable rescalings the ground state solutions \(u_{\varepsilon }\) of \((P_\varepsilon )\) converge to a particular solution of the critical local Emden–Fowler equation. The rescalings are implicit and depend in a non-trivial way on the exponent p and the space dimension \(N=3,4\) or \(N\ge 5\) . We establish a sharp asymptotic characterisation of such rescalings, as well as the blow-up rates or asymptotics of the \(L^2\) and other relevant norm of \(u_{\varepsilon }\) . As a follow up of our main results, we also obtain the existence, multiplicity and asymptotic behaviour of positive normalized solutions of a mass constrained problem associated to \((P_\varepsilon )\) with mass normalization constraint \(\int _{\mathbb {R}^N}|u|^2=c^2\) , as \(c\rightarrow 0\) and \(c\rightarrow \infty \) .
