をめぐって／をめぐる— Over the Matter Of

• その土地をめぐって、二つの村が争っている。

  Sono tochi o megutte, futatsu no mura ga arasotte iru.

  Two villages are in conflict over that land.

  土地 (land) + をめぐって marks the contested topic of the dispute.

• 新しい法律をめぐって激しい議論が続いた。

  Atarashii houritsu o megutte hageshii giron ga tsuzuita.

  A heated debate continued over the new law.

  法律 (law) + をめぐって shows the issue the debate centers on.

• 遺産をめぐる争いが家族を分裂させた。

  Isan o meguru arasoi ga kazoku o bunretsu saseta.

  The dispute over the inheritance split the family apart.

  をめぐる modifies 争い to mean 'the conflict concerning the inheritance'.

• ・Strongly implies conflicting opinions, debate, or competition around the topic.
• ・をめぐる is used before a noun; をめぐって works adverbially.
• ・Register: formal/written, common in news reports.

Commonly confused with

The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones をめぐって／をめぐる is tested against.

• ～一方だ — Heading Ever Further In One Direction
• ～がちだ — Prone To It
• ～からいうと／からいえば — Speaking In Terms Of
• ～からして — Even Just From
• ～かわりに — Instead Of / In Exchange
• ～きり — Only / And Never Since
• だらけ — Covered All Over
• っけ — What Was It Again?