The Board of Immigration Appeals, in a precedent decision clarifying Matter of Patel, has held that it does not retain jurisdiction over a case after remanding the record to an Immigration Court, and that an Immigration Judge is not required to hold a new hearing on remand unless the Board's order expressly directs one. Where a remand is unqualified, jurisdiction returns entirely to the Immigration Judge, who may conduct whatever further proceedings the remand order calls for, consistent with the INA and the regulations.
Applying that rule, the Board found no error in the Immigration Judge's decision to issue a new ruling denying withholding of removal and protection under the Convention Against Torture without convening an additional hearing, since the Board's remand order did not require one and the respondent had already received a full hearing before the case went up on appeal. The Board concluded that reassessing the existing record without reopening the evidentiary record did not violate due process or exceed the scope of the remand.
The full text of Matter of C-M-H-H- can be found here: https://www.justice.gov/eoir/media/1463836/dl?inline