  The electronic spin in quantum dots can be described by central spin models
(CSMs) with a very large number $N_\mathrm{eff} \approx 10^4$ to $10^6$ of bath
spins posing a tremendous challenge to theoretical simulations. Here, a fully
quantum mechanical theory is developed for the limit $N_\mathrm{eff} \to
\infty$ by means of iterated equations of motion (iEoM). We find that the CSM
can be mapped to a four-dimensional impurity coupled to a non-interacting
bosonic bath in this limit. Remarkably, even for infinite bath the CSM does not
become completely classical. The data obtained by the proposed iEoM approach is
tested successfully against data from other, established approaches. Thus, the
iEoM mapping extends the set of theoretical tools which can be used to
understand the spin dynamics in large CSMs.
