The Exchange System (Arbitration) Mailboxes, like ‘Discovery Search’ are created on the first Exchange server installed in the organization. If you need to remove a database or uninstall Exchange you will need to move the arbitration mailboxes to a different database or different server, respectively.

Command to search all databases for the arbitration mailboxes:
get-mailboxdatabase | Get-Mailbox -Arbitration |ft name,database,servername

Here is the command to determine if arbitration mailboxes are contained in a specific database:
Get-Mailbox –Database “Mailbox Database 1” –arbitration

Note: if your Exchange server is in a child domain it will appear that the arbitration mailboxes are missing. Use this command so that your get-mailbox commands will search all domains:
Set-ADServerSettings -ViewEntireForest:$true

Command to move all the arbitration mailboxes in the specified database to a new target database:

Get-Mailbox –Database “Mailbox Database 1” –arbitration | New-MoveRequest –TargetDatabase “Mailbox Database 2”

Check the status of the move and verify it has completed:
Get-MoveRequest

Note: If you are trying to uninstall one of your Exchange servers or remove a database and you haven’t moved the Arbitration mailboxes you may receive an error similar to the following: “This mailbox database contains one or more mailboxes, mailbox plans, archive mailboxes, or arbitration mailboxes.”