I will give the promised concluding part of an advanced class I gave last term on work with Tingxiang Zou, though assuming no memory of the first talk. I will briefly recall our conjectural description of non-expansion for families of birational maps, then focus on the ("de Jonquières") case of the action of the multiplicative group of unary rational functions on the plane by (x,y) |-> (x,f(x)*y), and similar situations.