Generally used in the Trope Launch Pad, this means that the person originating that topic wants to write any resulting article himself/herself, so this is a polite way of saying "Hands off, this is mine to write up and launch when I think it's ready.".
It goes without saying that No Launching Please includes Rolling Updates without that having to be stated separately.
The exact opposite of Up for Grabs.
If two or more months pass between updates by the original poster, the trope becomes Up for Grabs, as noted on that page.