Extremal shot noises naturally appear in extreme value theory as a model for
spatial extremes and serve as basic models for annual maxima of rainfall or for
coverage field in telecommunication. In this work, we examine their properties
such as boundedness, regularity, ergodicity ... Connexions with max-stable
random fields are established: we prove a limit theorem when the distribution
of the weights is heavy tailed and the intensity of points goes to infinity. We
use a point process approach strongly connected to the Peak Over Threshold
method used by hydrologists. Properties of the limit max-stable random fields
are also investigated.