Thanks Kyle,
According to what I read, the "PHP Mail function" requires that a MTA be installed. My Server does not have one. Neither Sendmail nor Postfix is installed. Yet email goes through from Joomla and CB.
How would the "PHP Mail function" know that my mail is handled via another server. php.ini does not point to the 1and1 server... Probably from the domain name itself via DNS... strange.
1and1 says that the "apache@..." address is generated via reverse mapping and that the only place where to change the return address is probably in joomla.
I switch to "smtp server" as my mailer in global settings and everything works as it should.
Conclusion: Even though email is sent from the "PHP Mail function" without a local mail server... It is probably indispensable to have one to make it work right.
Thanks