If my fiance and i have a family friends Two Year Old for weeks at a time?

The child goes home maybe two to three days out of a month we have been getting this baby since mid december of 2009. And shes with us all month expect a couple days when her grandmother wants to see her. The child calls my fiance and myself daddy and mommy and her birth parents by their names. They have signed papers at the doctors office giving us premission to take her to the doctor and being able to get any medical records. Whats our chances of getting custody over her ? Could we file for emergency custody ?