One aspect of opinion change that has been of academic interest is the impact of people with extreme opinions (extremists) on opinion dynamics. An agent-based model has been used to study the role of small-world social network topologies on general opinion change in the presence of extremists. It has been found that opinion convergence to a single extreme occurs only when the average number of network connections for each individual is extremely high. Here, we extend the model to examine the effect of positively skewed degree distributions, in addition to small-world structures, on the types of opinion convergence that occur in the presence of extremists. We also examine what happens when extremist opinions are located on the well-connected nodes (hubs) created by the positively skewed distribution. We find that a positively skewed network topology encourages opinion convergence on a single extreme under a wider range of conditions than topologies whose degree distributions were not skewed. The importance of social position for social influence is highlighted by the result that, when positive extremists are placed on hubs, all population convergence is to the positive extreme even when there are twice as many negative extremists. Thus, our results have shown the importance of considering a positively skewed degree distribution, and in particular network hubs and social position, when examining extremist transmission.