Influence starbases

When you construct an influence starbase it increases your influence by a percentage.  Does the starbase's influence ring have to be around a planet for that planet's influence to increase or does it just increased influence whereever it is placed?  I just realized that I've been thinking it just increases my influence wherever I place it, but maybe it works like the economy starbases that increase the trade amount of the routes that pass through its ring of influence.

Any insight into this would be great.  Thanks!

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Influence starbases don't increase the influence of any planets in the ring, it only increases its own influence. You can place one deep in an AI's territory to open a "bubble" of your territory, even if you don't own a planet anywhere nearby.

Also, the influence from a base drops off faster than it does with a planet. Planet incluence seems to drop off nearly linearly with distance, while base influence drops at closer to distance squared. The important thing to take from this is that an influence base is most effective when built touching the planet you want to influence.