28 U.S.C. § 2251 : US Code - Section 2251: Stay of State court proceedings

Search 28 U.S.C. § 2251 : US Code - Section 2251: Stay of State court proceedings

A justice or judge of the United States before whom a habeas
corpus proceeding is pending, may, before final judgment or after
final judgment of discharge, or pending appeal, stay any proceeding
against the person detained in any State court or by or under the
authority of any State for any matter involved in the habeas corpus
proceeding.
After the granting of such a stay, any such proceeding in any
State court or by or under the authority of any State shall be
void. If no stay is granted, any such proceeding shall be as valid
as if no habeas corpus proceedings or appeal were pending.