Influence Starbases project influence like a planet. Various modules improve this ability. It amplifies the effect of your influence in parsecs inside its radius, just like a Military Starbase amplifies attack and defence. All starbases have some sort of influence-creating ability inherent to them, because mining starbases I put down always have a zone of my influence around them. (The strongest influence effects of course come from the influence modules, but do they just add to the background influence or do they multiply it? --Varis)