Hi. it is most likey HPV. you can researh that all day long. Truth is these warts are there because the virus could not be fought off by her immune system and thus comes through by way of warts. They say it is a disease that could have been past through the womb and could have laid dormant all this time and finally came up now. She could have gotten it from playing with other children who have HPV. There are hundreds of strands of this virus and it is contagous. Normally the warts will last for upto 2 years and eventually go away. It may be bothering you more than her but if you want it to go away asap, tell the dermatologist to freeze it with liquid nitrogen. My son had it done and it is absolutely painless!!! Good luck.