  Start with a graph with a subset of vertices called {\it the border}. A
particle released from the origin performs a random walk on the graph until it
comes to the immediate neighbourhood of the border, at which point it joins
this subset thus increasing the border by one point. Then a new particle is
released from the origin and the process repeats until the origin becomes a
part of the border itself. We are interested in the total number $\xi$ of
particles to be released by this final moment.
  We show that this model covers OK Corral model as well as the erosion model,
and obtain distributions and bounds for $\xi$ in cases where the graph is star
graph, regular tree, and a $d-$dimensional lattice.
