Partitioning a tournament into sub-tournaments of high connectivity

We prove that there exists a constant $c>0$ such that the vertices of every strongly $c\cdot kt$-connected tournament can be partitioned into $t$ parts, each of which induces a strongly $k$-connected tournament. This is clearly tight up to a constant factor, and it confirms a conjecture of Kühn, Osthus and Townsend (2016).