The spell Black Tentacles does not say how high they can reach up. Could it grab some Stirges that fly over the area of effect for example?
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Yes, it could, unless the stirges are flying over 20' high - at the spells centrepoint anyway.
The SRD clarifies that any spell with a radius extends into the third dimension in a similar fashion.
Black tentacles has a 20' radius of effect and only effects creatures in the area of effect, therefore as long as the stirges have room to fly above that height they're safe, otherwise they're going to get grabbed.
Since the effect is a sphere they could squeeze past in a corner if there's room, I'd give them a flying roll for this to not miss a flap and become tenticalificed.
This does create another question however, how high do spells extend if they have an area of effect but don't have a radius (looking through a load of AOE spells they seem to have done a good job of covering this actually, most spells have a height specified or are a radius effect) Maybe I need a question "how high is a square?"