 Trifurcation vertex in percolation

A trifurcation graph vertex is a graph vertex of an infinite percolation cluster whose deletion separates that cluster into at least three infinite connected components of a graph. In a finite modification argument one may make it have exactly three open incident edges leading to three different infinite components. On a translation-invariant lattice, a positive probability of trifurcation at one graph vertex gives a positive expected density of trifurcations.