"Race to the courthouse" is an informal name

Colloquialism

A colloquialism is a word or phrase that is common in everyday, unconstrained conversation rather than in formal speech, academic writing, or paralinguistics. Dictionaries often display colloquial words and phrases with the abbreviation colloq. as an identifier...

 used to describe the rule in some jurisdictions that the first conveyance instrument, mortgage, lien

Lien

In law, a lien is a form of security interest granted over an item of property to secure the payment of a debt or performance of some other obligation...

or judgment to be filed with the appropriate recorder's office, will have priority and prevail over documents filed subsequently, irrespective of the date of execution of the documents at issue.