  We consider a general preferential attachment model, where the probability
that a newly arriving vertex connects to an older vertex is proportional to a
sublinear function of the indegree of the older vertex at that time. It is well
known that the distribution of a uniformly chosen vertex converges to a
limiting distribution. Depending on the parameters, this model can show power
law, but also stretched exponential behaviour. Using Stein's method we provide
rates of convergence for the total variation distance. Our proof uses the fact
that the limiting distribution is the stationary distribution of a Markov chain
together with the generator method of Barbour.
