Remove All Exchange 2010 Disconnected Mailboxes

$mailboxes = Get-ExchangeServer | Where-Object {$_.IsMailboxServer –eq $true} | ForEach-Object { Get-MailboxStatistics –Server $_.Name | Where-Object {$_.DisconnectDate –notlike ‘’}} | select displayname, mailboxguid, database
$mailboxes | ForEach { Remove-Mailbox -Database $_.Database -StoreMailboxIdentity $_.MailboxGuid -confirm:$false }
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Set Send on Behalf of Distribution List
Set-DistributionGroup -Identity GroupName -GrantSendOnBehalfTo User1,User2
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Manually Update global address book
Get-GlobalAddressList | Update-GlobalAddressList
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Remove a distribution group
Remove-DistributionGroup -Identity "GROUP ALIAS"

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Get Database size
Get-MailboxDatabase -Status | select ServerName,Name,DatabaseSize

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Shows mailbox sizes on Exchange 2007 and 2010
Get-MailboxStatistics -Server 'SERVER' | where {$_.ObjectClass -eq “Mailbox”} | Sort-Object TotalItemSize -Descending | ft @{label=”User”;expression={$_.DisplayName}},@{label=”Total Size (MB)”;expression={$_.TotalItemSize.Value.ToMB()}}  -auto >> "c:\mailbox_size.txt"

Another simply way to get the size without using the download file - tested on Exchange 2013 only
Get-MailboxStatistics -Server SERVER | Sort-Object TotalItemSize -Descending | ft DisplayName,@{label=”TotalItemSize(MB)”;expression={$_.TotalItemSize.Value.ToMB()}}  -auto
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Helpful Commands to export mailboxes on Exchange 2010 and above to a PST file like ExMerge once did
http://technet.microsoft.com/en-us/library/ff607299%28v=exchg.150%29.aspx

New-MailboxExportRequest -Mailbox ALIAS -FilePath "\\unc-path\FOLDER\Saved-Stuff.pst"

Get-MailboxExportRequestStatistics -Identity ALIAS\MailboxExport1

Don't forget to add the Mailbox Export / Import role otherwise the before mentioned website commands will not work
1.) In the EAC, navigate to Permissions > Admin Roles.
2.) Select the role group you want to add a role to, and then click Edit Edit icon.
3.) In the Roles section, select the roles you want to add to the role group.
4.) When you’ve finished adding roles to the role group, click Save.