https://en.wikipedia.org/wiki/Title_search
In real estate business and law, a title search or property title search is the process of retrieving documents evidencing events in the history of a piece of real property, to determine relevant interests in and regulations concerning that property.

https://definitions.uslegal.com/t/title-examination/
Title examination is a close examination of all public records that affect the title to the real estate you are purchasing. The search involves reviewing past deeds, wills, and trusts to make sure the title has passed correctly to each new owner. The examiner tries to verify that all prior mortgages, judgments, and other liens have been paid in full.