Factor of iid’s through stochastic domination

We develop a method to prove that certain percolation processes on amenable random rooted graphs are factors of iid, given that the process is a monotone limit of random finite subgraphs that satisfy a certain independent stochastic domination property. Among the consequences is the previously open claim that the Uniform Spanning Forest is a factor of iid for recurrent graphs, and that it arises as a finitary factor.