Anal warts, which are caused by HPV, can be removed by a doctor or with treatments applied at home. Depending on which treatment is used, there is a 10-30% chance of the warts coming back. Some people have only one outbreak of warts, others have recurrences over time.
Genital warts are most likely to be transmitted to your sex partners when the warts are actually present but sometimes warts are too small to easily see. Very little is known about passing HPV to sex partners if the virus is present but no warts can be seen. It is possible that your partner has already been exposed to this strain of HPV but didn't get any warts.
There is no way to know for sure though because there are currently no HPV tests for men. There is an excellent vaccine that protects against 9 of the most common strains of HPV -including 4 high-risk strains and 5 strains that can cause warts. Its recommended that all men and women <26 receive this vaccine. If you or your boyfriend have not already been vaccinated, you should talk to your providers about getting vaccinated.