The variability in topological shapes of observed neuronal branching patterns can accurately be described by a simple model for random sequential growth. This finding is remarkable in view of the fact that the actual neuritic growth process can vary, and includes phases of regression and removal of branches which were not considered in the model. The aim of the present study is to investigate the influence of removal of branches on the topological structure of branching patterns as well as the effect of variable growth rules. A tree asymmetry index is used for the characterization of the topological structure of a tree. The mean value of the asymmetry index for a set of dendritic trees is sensitive to the mode of growth. The effect of removal of branches ("pruning") on the topological structure of dendritic trees has been studied for several random pruning schemes, namely (i) removal of uniform randomly chosen subtrees, (ii) removal of uniform randomly chosen terminal segments, (iii) uniform random pruning during the growth process itself, and (iv) non-uniform random pruning schemes. It was found that the effect of pruning depends on both the mode of pruning and the mode of growth. Uniform random (terminal) pruning had no effect on the mean and standard deviation of the asymmetry index of trees grown with an order-independent mode of branching. Changes in the mean of the asymmetry index could occur either with non-uniform random pruning or when trees are grown according to an order-dependent mode of branching. The effect of variable growth rules was studied for several specific schemes, and it could be shown that they all result in a substantial increase in the variation in the asymmetry index of the trees.