I have been with my husband 3 years now, legally married for 2. I have 4 children from my first marriage. Their biological father left the country to avoid paying child support & never gave a $.01. My husband & I would love for him to adopt them all & carry all the same last name. How can I go about doing this in the state of Texas? What process do we need to go through & what is the estimated cost?

You will hire an attorney,
Attempts have to be made to contact the father and get his consent for the adoption.
If he can not be found, public notification will be done.

Court will review to be sure that proper attempts to find him was made and done.
If found, and he does not give consent, he will have right to represent in court why the adoption should not happen.

You will present good reason for it to happen.
** his non payment and non visit is not the good reason, there has to be other reasons according to state law that the attorney will help you figure out.

Four children, without consent of father, most likely in the 10,000 to 15,000 dollar range.