We introduce the multiplicative coalescent with linear deletion, a continuous-time Markov process describing the evolution of a collection of blocks. This process arises in connection with  random graph models which exhibit self-organised criticality.  We focus on results describing states of the process in terms of collections of excursion lengths of random functions, in which the coalescence of blocks is related to a "tilt" of the random function and deletion of blocks is related to a "shift" of the random function. Joint work with James Martin.