This is joint work with Abert and Fraczyk. Given a percolation E of the Cayley graph of a group G (thought of as a random subgraph), Burton-Keane and Lyons-Schramm showed the existence of the trajectory density, which is the almost sure limit (1/n)|\&ob;1\leq j\leq n:g_&ob;1&cb;\cdots g_&ob;j&cb; is connected to the identity in E&cb;|. for a random walk g_&ob;1&cb;\cdots g_&ob;j&cb; in the Cayley graph of G. Moreover, this limit is a.s. independent of the random walk. We give a separate proof of this result in the more general context of inclusion of equivalence relations S inside of R (where R is given by a free action of G). Moreover, we give a complete computation of this quantity in terms of the index of R restricted to the ergodic components of the subrelation. When G has Property (T) we show that zero trajectory density implies a uniform upper bound (independent of S) on the co-spectral radius (in the sense of our previous work) of S inside of R.