I want to set sendmail up as a mail gateway.

I have several Email systems for different groups and I want to be able =
to tell everyone to set there email up as user@name.com though their =
real email may be user@machine.name.com.

Basically the way if see it working is:

1) If someone sending email knows their real email address =
(user@machine.name.com) or is replying to a message, everything will =
work the same.

2) When I add an account to a 2ndary machine I want to be able to just =
tell them that their email is user@name.com.

So what will happen if an Email gets sent to the primary email machine =
and the user is unknown, it will pass it on to Email system2, which will =
try to find a home for it, if the user is unknown, pass it on to system3 =
and so forth until it gets to a terminal (end) email system which will =
send the sender a no such user email.

Now to do this, would each machine have to re-hash the To: address =
before sending it on?