To kill a zombie (process) you have to kill its parent process (just like real zombies!), but the question was how to find it.
Find the zombie (The question answered this part):
a@SERVER:~$ ps aux | grep 'Z'
What you get is Zombies and anything else with a Z in it, so you will also get the grep:
USER PID %CPU %MEM VSZ RSS TTY STAT START TIME COMMAND
usera 13572 0.0 0.0 7628 992 pts/2 S+ 19:40 0:00 grep –color=auto Z
usera 93572 0.0 0.0 0 0 ?? Z 19:40 0:00 something
Find the zombie's parent:
a@SERVER:~$ pstree -p -s 93572
Will give you:
init(1)—cnid_metad(1311)—cnid_dbd(5145)
In this case you do not want to kill that parent process and you should be quite happy with one zombie, but killing the immediate parent process 5145 should get rid of it.
Additional resources on askubuntu: