If your sendmail is in HP-UX default configuration, it will use the Mail Exchanger records in the DNS system to find the relay server separately for each destination address. Effectively, it's trying to deliver each mail as directly as possible to the recipient's mail server.
To run the equivalent DNS query manually, find the FQDN part of the mail address and run nslookup on it using the "-query=mx" option.
For example, if the mail recipient is "Joe.Blow@company.example", then run:
nslookup -query=mx company.example
If there are no MX records in the DNS for the mail recipient, sendmail will (by default) try to contact the recipient host (here "company.example") directly. If that fails too, the mail is undeliverable and a bounce message will be sent to the sender.
In these days, it's the standard practice to allow only the organization's "main" mail server(s) to work like that: all the others are usually configured to send all outgoing mail to the main server(s) only. This is called a "smart host configuration".
Open /etc/mail/sendmail.cf using your favorite editor and search for the string "DS" in all-caps. You'll find a lot of comments describing how to set the smart host configuration, and after the comments, the actual configuration line:
# "Smart" relay host (may be null)
DS
If there is no hostname or IP address after the letters "DS", smart host is not configured.
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