  We consider the Bernoulli percolation model in a finite box and we introduce
an automatic control of the percolation probability, which is a function of the
percolation configuration. For a suitable choice of this automatic control, the
model is self-critical, i.e., the percolation probability converges to the
critical point $p_c$ when the size of the box tends to infinity. We study here
three simple examples of such models, involving the size of the largest
cluster, the number of vertices connected to the boundary of the box, or the
distribution of the cluster sizes.
