Step parent Adoption

I just have a question about adoption. If somebody wants to adopt his/her spouse's children, paano po yung process? I have 2 kids and I am not married to the bio father. The bio father left a few months after the 2nd child was born pero nakapirma pa siya sa birth cert ng 2 bata. I'm about to get married, and my husband to be is planning to adopt them. One reason is for them to avoid confusion sa mga last names namin. Also para maging legal parent na siya ng mga bata. Meron din ako nabasa na mga forum saying na we need the bio father to sign. He's nowhere to be found na. Pwede ba maging grounds ang abandonment and skip yung signature ng bio father?

begin with looking for the adoption thread here where there is a list of docu requirements. yes, you can allege abandonment