Before revision:   In particular, we find a nonlinear scaling of the mean {\em   number of particles accumulated at the tip ( tip size ) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system .
After revision:  In particular, we find a nonlinear scaling of the mean {\em number of particles accumulated at the tip  tip size ) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system .