Unavoidable stars in 3-graphs

Suppose $\text{F}$ is a collection of 3-subsets of {1,2,…,n}. The problem of determining the least integer $\text{?(n, k)}$ with the property that if $\text{|F| > ?(n, k)}$ then $\text{F}$ contains a k-star (i.e., k 3-sets such that the intersection of any pair of them consists of exactly the same element) is studied. It is proved that, for k odd, $\text{?(n, k) = k(k ? 1)n + O(k}{}^3\text{)}$ and, for k even, $\text{?(n, k) = k(k ?}\text{3}\text{2}\text{)n + O(n + k}{}^3\text{)}$.