  We study properties of relative types of plurisubharmonic functions with
respect to maximal plurisubharmonic weights. It is shown that they give a
general form for upper semicontinuous, tropically additive functionals on
plurisubharmonic singularities. We consider some extremal problems whose
solutions are Green-like functions that give best possible bounds on a
plurisubharmonic function, given the values of its types relative to some of
(or all) the weights. An analyticity theorem is proved for the upperlevel sets
for the types with respect to exponentially H\"older continuous weights, which
leads to a result on propagation of plurisubharmonic singularities.
