  We continue our study of string correlators on Euclidean $\text{AdS}_3$ with
pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic
structure, which we analyse completely for genus 0 four-point functions. We
show that correlators exhibit a simple behaviour near their singularities. The
spacetime correlators are meromorphic functions in the
$\mathrm{SL}(2,\mathbb{R})$-spins, whose pole structure is shown to agree with
the prediction of a recent proposal for the dual $\text{CFT}_2$. Moreover, we
also compute the residues of the spacetime correlators for some of the poles
exactly and find again a perfect match with the proposal for the dual
$\text{CFT}_2$, thereby checking the duality for some non-trivial four-point
functions exactly. Our computations simplify drastically in the tensionless
limit of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$ where the
behaviour near the poles gives in fact the exact answer. This paper is the
third in a series with several installments.
