Bin sizes in time-inhomogeneous infinite Polya processes

At the nnth step of a time-inhomogeneous infinite Polya process, either a new bin is created and a ball is put in that bin, or a ball is put into an existing bin, in which case the bin is chosen according to a preferential attachment type rule. We introduce a new class of such processes and find the asymptotics of the expected number of bins of size kk, for kk fixed, as n→∞n→∞.