From the Eclipse rulebook, page 21:
Influencing hexes: If a hex has no population after all battles have been resolved and you have at least one Ship there, remove the previous controller’s Influence Disc (returning it to his Influence Track). After this, you may place your own Influence Disc there. Also, if your Ship is in a hex without an Influence Disc after the Combat Phase, you may place a disc there.
A literal interpretation of the last sentence means that just having a ship in a hex allows one to stake a claim with an Influence Disc. Obviously, this would apply for the following two combat-related situations:
- Defeating ancients or the GCDS, leaving behind an unclaimed hex.
- Two opposing armies fighting over an uncontrolled hex, leaving behind an unclaimed hex.
However, this also opens up a third intriguing possibility:
- Moving a ship into an unclaimed and uncontested hex, later claiming it without needing an Influence action.
Is this third interpretation legal, or are hexes claimed in this step limited only to ships which actually did something during the Combat Phase?