There is no question that current or recent smoking raises the odds.
But the causal link appears to be less clear for people who quit smoking, depending on how long ago they stopped. For example, my husband -- not a heavy smoker to begin with -- quit more than 20 years ago, and his doctor at Hopkins CCC says he considers him to be in the same "category" as patients who have never smoked.
As for
HPV, a CDC web page about the new vaccine, Gardasil, notes that it is possible for the virus to remain in a non-detectable dormant state and then reactivate many years later.
So who knows?