Even though aircraft icing has been an active area of research for many years due to its public safety ramifications, there are still gaps in the knowledge base, such as in the ice accretion process. Ice prediction codes have been developed and generally can capture the gross features of the ice shape for many areas of parameter space. However, there are still features of the ice shapes that are not captured and not well understood. For example, current icing codes have difficulty in predicting the ice or frost that develops beyond the impingement limits from a standard trajectory analysis. This is a strong indicator that there are other physical mechanisms that lead to ice growth in these areas, which require further investigation. The present study focuses on the effects of relative humidity and shed vortices from the ice surface on the downstream ice growth. Relative humidity was found to be a secondary effect in the direct impingement regions due to the time scales involved. However, exposure to supersaturated air for long periods can lead to localized ice/frost growth aft of the primary ice shape. It was also found that the vortices shed from ice surface or vortices entrapped within the ice roughness can alter the trajectory paths of the droplets and potentially change the ice growth process. The altered paths result in impingement on areas that are beyond the direct impingement region.