Each component of the pipeline will be a child process of the shell. If you use pstree -p
from another terminal, you'll probably see something like this:
...
sshd(11)---bash(12)-+-ls(13)
|-grep(14)
\-wc(15)
...
(assuming you can run this whilst your pipeline is still running!)
However, note that all the components will form a single process group.
The piping itself is a feature of Linux (or whatever OS you're using), it's not a separate user process. The shell creates some anonymous pipes, and hooks them up to the relevant file descriptors for each pair of processes in the pipeline.