  We propose a generalized model for uniform recursive tree (URT) by
introducing an imperfect growth process, which may generate disconnected
components (clusters). The model undergoes an interesting phase transition from
a singly connected network to a graph consisting of fully isolated nodes. We
investigate the distributions of degree and component sizes by both theoretical
predictions and numerical simulations. For the nontrivial cases, we show that
the network has an exponential degree distribution while its component size
distribution follows a power law, both of which are related to the imperfect
growth process. We also predict the growth dynamics of the individual
components. All analytical solutions are successfully contrasted with computer
simulations.
