AD Forests Trusts

I have a Windows 2003 Active Directory domain setup, with all necessary users, groups, permissions, group policy, etc.

I would like to setup a two-way trust between my domain and another domain in a separate forest.

My question is this: If I setup this trust, will the domain administrator(s) in the other domain/forest have domain admin privileges in my domain/forest automatically? Or would I have to manually add those admins to my admins group?

Thanks in advance for any help.