Linear trees in uniform hypergraphs

Given a tree T on v vertices and an integer k≥2 one can define the k-expansion T(k) as a k-uniform linear hypergraph by enlarging each edge with a new, distinct set of k−2 vertices. T(k) has v+(v−1)(k−2) vertices. The aim of this paper is to show that using the delta-system method one can easily determine asymptotically the size of the largest T(k)-free n-vertex hypergraph, i.e., the Turán number of T(k).