How to get the id of a very short child process iw the parent is known?

view story

http://unix.stackexchange.com – I'm looking for a way to get the pid of a short child process. The process is instant from a human perspective. I know the parent process which will spawn the child process. Is there a way to log information about all the processes that are created by a specific parent process? I'm not looking for a way to retroactively figure out the pid of the child but a way to log it once it happens. (HowTos)