If somebody has warts that were treated, are they contagious in the future?

I don't think there is a clear answer on this one. It is really unknown it is known that someone can share the virus years after they acquired the virus. It is also known you can acquire other HPV types, HPV types 6 and 11 cause most genital warts, a person can build immunity to HPV type 6 then acquire HPV type 11 from a new sex partner. They are other HPV types that can cause visible warts. They are 40 HPV types. It is really unknown when a person develops warts years after an out break if it is a reawaken of the virus acquired years before or if you have acquired a new HPV type. Many men and women have multiple HPV types. The virus can go from a latent state to an express state years later.

The virus enters the skin tissue.

Most men and women do build immunity to their acquired HPV type in about 2 years. It is also known that in some the virus can escape the immunity it obtain.

Condoms do help in the prevention but they are not 100%. Most men and women will acquire an HPV type at some time in their life.

http://www2a.cdc.gov/stdtraining/self-study/hpv/cd...

Longitudinal studies in both men and women show that the concurrent or sequential detection of more than one HPV type is common, and that this occurs more frequently than would be expected by chance

http://www.medscape.com/viewarticle/553264_5

1