"Register user" function

Hi,

I'm looking for the function that actually decide that an user is fully registered. I need help.
This will be the exact location for me to enter some php lines to register the same user in a phpbb forum under the same login with the same password & mail.

In other words, I would like my users to register only once to use both Drupal website and the forum.

And I also need to register them into Drupal's database if they choose to register using the forum....

I really need your help to complete these two difficult tasks. Thank you.