  We consider 2D networks composed of nodes initially linked by two-qubit mixed
states. In these networks we develop a global error correction scheme that can
generate distance-independent entanglement from arbitrary network geometries
using rank two states. By using this method and combining it with the concept
of percolation we also show that the generation of long distance entanglement
is possible with rank three states. Entanglement percolation and global error
correction have different advantages depending on the given situation. To
reveal the trade-off between them we consider their application on networks
containing pure states. In doing so we find a range of pure-state schemes, each
of which has applications in particular circumstances: For instance, we can
identify a protocol for creating perfect entanglement between two distant
nodes. However, this protocol can not generate a singlet between any two nodes.
On the other hand, we can also construct schemes for creating entanglement
between any nodes, but the corresponding entanglement fidelity is lower.
