yes traditionally thought-once you have genital warts/ hpv you always have it even when symptoms are not present- virus lay dormant. taking out the cervix / uterus does not have bearing on whether you are still infected. the warts can be inside the vagina/in or near anus (butt) and can still transmit especially after having sexual contact- microscopic cuts occur which allows the virus to pass from one person to another and therefore risking infecting the other person. treatments to remove the warts are available however even if there are no visual warts doesn't mean the virus is out of the body. if you have new partners either have relations with dormant like yourself or let other person know your situation and let him/her make the decision to take risk. then again what do i know?
if you have no cervex or uterus and have not had a symtom or outbreak of genital warts in 20 yrs are you still infected