You're clear of future infections. Your antibodies will help protect you in the future if you come across the virus again.
As zellyf said, your results look good:
Hep B Sur Ag ... Negative =You don't have HBV
Hep B Sur Ab ... Positive =You are immune
Hep B Core Ab ... *Positive =Sometime ago you had HBV but you cleared it
Anti-Hep C Ab ... Negative =You do not have HCV
You don't have HBV, so there is nothing to completely remove and nothing to spread.
According to what you have posted, you do not have Hep B. You are negative for the surface antigen and you have antibodies. At some point you had an acute infection and your body cleared it on its own. If you had sex with someone while you were acute you could have given them the virus (or gotten it that way if you had sex with someone who was infected) but you are no longer infected and are, in fact, immune. Congratulations!