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Description:  

Determines whether users can delete all user remote access connections.

To create an all-user remote access connection, on the Connection Availability page in the New Connection
Wizard, click the "For all users" option.

If you enable this setting, all users can delete shared remote access connections. In addition, if your file
system is NTFS, users need to have Write access to Documents and Settings\All Users\Application Data
\Microsoft\Network\Connections\Pbk to delete a shared remote access connection.

If you disable this setting (and enable the "Enable Network Connections settings for Administrators" setting),
users (including administrators) cannot delete all-user remote access connections. (By default, users can still
delete their private connections, but you can change the default by using the "Prohibit deletion of remote
access connections" setting.)

Important: If the "Enable Network Connections settings for Administrators" is disabled or not configured, this
setting will not apply to administrators on post-Windows 2000 computers.

If you do not configure this setting, only Administrators and Network Configuration Operators can delete all
user remote access connections.

Important: When enabled, the "Prohibit deletion of remote access connections" setting takes precedence
over this setting. Users (including administrators) cannot delete any remote access connections, and this
setting is ignored.

Note: LAN connections are created and deleted automatically by the system when a LAN adapter is installed
or removed. You cannot use the Network Connections folder to create or delete a LAN connection.

Note: This setting does not prevent users from using other programs, such as Internet Explorer, to bypass
this setting.

Supported on: Windows Server 2003, Windows XP, and Windows 2000 operating systems only.
Ability to delete all user remote access
connections
Description Gpedit Regedit CMD Back VBScript PowerShell Script
Gpedit:   

Please perform the following steps:

Please go to Pearl button (Start) and click on the Search programs and files
For more information about the change from Start to Pearl button click here
Type gpedit.msc and press Enter
In the Group Policy window please navigate to User Configuration -> Administrative Templates ->
Network -> Network Connections and open Ability to delete all user remote access connections.
Not Configured -> is the Default state
Enabled -> apply this GPO
Disabled -> this GPO will not be applied

To finish press ok button and close Group Policy window.
Type regedit and press ok
Please confirm User Account Control pop-up
Microsoft official disclaimer

Warning Serious problems might occur if you modify the registry incorrectly by using Registry Editor or by
using another method. These problems might require that you reinstall the operating system. Microsoft
cannot guarantee that these problems can be solved. Modify the registry at your own risk.

Note: This registry key is created by Group Policy when this GPO is Enable. The GPO Default state is Not
Configured -> this registry entry is not present. For Disable this registry entry is not present.

Please navigate to HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\Network Connections
and locate NC_DeleteAllUserConnection registry key
Regedit:          

Please perform the following steps:

Please go to Pearl button (Start) and click on the Search programs and files
For more information about the change from Start to Pearl button click here
   
   
Double click on NC_DeleteAllUserConnection and edit the value:

To Enable:
Change the data value with:
NC_DeleteAllUserConnection = 1

To Disable:
Change the data value with:
NC_DeleteAllUserConnection = 0

To finish press ok button and close Registry Editor window

Note: Manual editing of this registry key will not be reflected in Group Policy. If you modify this GPO from
Group Policy this registry key will be rewritten.
Type cmd, right click on cmd icon under the Programs and click on Run as administrator
Please confirm User Account Control pop-up
Please select, right and copy a registry key from below, then right click on command prompt window
, select Paste and press Enter

Enabled:
REG add "HKCU\Software\Policies\Microsoft\Windows\Network Connections" /v NC_DeleteAllUserConnection /t REG_DWORD /d 1 /f

Disabled:
REG add "HKCU\Software\Policies\Microsoft\Windows\Network Connections" /v NC_DeleteAllUserConnection /t REG_DWORD /d 0 /f

Not Configured:
REG DELETE "HKCU\Software\Policies\Microsoft\Windows\Network Connections" /v NC_DeleteAllUserConnection /f

Note: Manual editing of this registry key will not be reflected in Group Policy. If you modify this GPO from
Group Policy this registry key will be rewritten.
CMD:          

Please perform the following steps:

Please go to Pearl button (Start) and click on the Search programs and files
For more information about the change from Start to Pearl button click here
   
VBScript:          

Const HKEY_CURRENT_USER = &H80000001
strComputer = "."
Set oReg=GetObject("winmgmts:{impersonationLevel=impersonate}!\\" & _
strComputer & "\root\default:StdRegProv")

strKeyPath = "Software\Policies\Microsoft\Windows\Network Connections"
oReg.CreateKey HKEY_CURRENT_USER,strKeyPath
strValueName = "NC_DeleteAllUserConnection"
'Enabled
dwValue = 0
'Disabled
'dwValue = 1
oReg.SetDWORDValue HKEY_CURRENT_USER,strKeyPath,strValueName,dwValue
'Not Configured
'oReg.DeleteValue HKEY_CURRENT_USER,strKeyPath,strValueName
   
PowerShell Script :          

Enabled

$RegKey = "HKCU:\Software\Policies\Microsoft\Windows"
If(Test-Path ($RegKey + "\Network Connections"))
{
 $RegKey = "HKCU:\Software\Policies\Microsoft\Windows\Network Connections"
  ##Enabled
  New-ItemProperty -path $RegKey -name NC_DeleteAllUserConnection -value 1 -PropertyType DWord -Force
  ##Disabled
  ##New-ItemProperty -path $RegKey -name NC_DeleteAllUserConnection -value 0 -PropertyType DWord -Force
}
else
{
 New-Item -path $RegKey -name "Network Connections"
 $RegKey = "HKCU:\Software\Policies\Microsoft\Windows\Network Connections"
  ##Enabled
  New-ItemProperty -path $RegKey -name NC_DeleteAllUserConnection -value 1 -PropertyType DWord
  ##Disabled
  ##New-ItemProperty -path $RegKey -name NC_DeleteAllUserConnection -value 0 -PropertyType DWord
}

Not Configured\Disabled

$RegKey = "HKCU:\Software\Policies\Microsoft\Windows"
Remove-ItemProperty -Path($RegKey + "\Network Connections") -name NC_DeleteAllUserConnection
If( (Get-Item -Path($RegKey + "\Network Connections")).ValueCount -eq 0 -and (Get-Item -Path($RegKey + "\Network Connections")).SubKeyCount -eq 0)
{
 Remove-Item -Path($RegKey + "\Network Connections")  
}
   
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Result:

Need test pictures.
Verify code.
Result