The following is a list of all board game mechanics I know in this category, and that aren’t too niche. Card game mechanics are also included. I’m posting this mainly for my own reference.

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Area Majority / Influence: Multiple players may occupy a space and gain benefits based on their proportional presence in the space.

In El Grande, for instance, players earn their score in a region by having the most caballeros in that region.

Enclosure: In Area Enclosure games, players place or move pieces in order to surround areas contiguously with their pieces. The oldest and most famous Area Enclosure game is of course Go, but many newer examples also exist.

Area Enclosure is different than Area Majority / Influence because players actually create the areas on a gridded board during the course of play, whereas in Area Majority/Influence the actual areas are pre-existing and players are merely competing control over them.

King of the Hill: Games with a king of the hill mechanism reward players with points or other advantages for occupying a special position on the board. How long can you hold your ground?

Ownership: Players own entities, and perform actions for those entities, or collect benefits if others use them. Le Havre and Caylus allow players to own action spaces, and gain a benefit when other players use them.

Static Capture: Pieces are captured when another piece occupies or passes over their space.