The uniform Turán density of large stars

We asymptotically resolve the the uniform Turán density problem for the large stars. In particular, we show that the uniform Turán density of the $k$-star $S_k$ is $\frac{k^2-5k+7}{(k-1{)}^2}$ for $k\ge 48$, matching a lower construction by Reiher, Rödl and Schacht.