stake out a claim to
stake out a claim to (something)
To assert one's right to or ownership of something. My great-grandfather staked out a claim to this land over 100 years ago. You can't have this cookie because someone else already staked out a claim to it. Settlers arrived in droves looking to stake out claims to the newly discovered land.
stake out a claim to somethingand stake out a claim on something
to lay claim to something. The prospector staked out a claim to the promising piece of land. We staked out a claim on two seats at the side of the auditorium.