  We study the generation of singlets in quantum networks with nodes initially
sharing a finite number of partially entangled bipartite mixed states. We prove
that singlets between arbitrary nodes in such networks can be created if and
only if the initial states connecting the nodes have a particular form. We then
generalize the method of entanglement percolation, previously developed for
pure states, to mixed states of this form. As part of this, we find and compare
different distillation protocols necessary to convert groups of mixed states
shared between neighboring nodes of the network into singlets. In addition, we
discuss protocols that only rely on local rules for the efficient connection of
two remote nodes in the network via entanglement swapping. Further improvements
of the success probability of singlet generation are developed by using
particular forms of `quantum preprocessing' on the network. This includes
generalized forms of entanglement swapping and we show how such strategies can
be embedded in regular and hierarchical quantum networks.
