  We study normalised solutions for a Choquard equation in the plane with
polynomial Riesz kernel and exponential nonlinearities, which are critical in
the sense of Trudinger-Moser. For all prescribed values of the mass, we prove
existence of a positive radial solution by a variational argument, which
exploits a delicate analysis on the mountain pass level. Under an additional
monotonicity assumption on the nonlinearity, such a solution turns out to be
also a ground state in $H^1(\mathbb R^2)$. Our work extends in several
directions the results by Deng-Yu.
