I would highly advise using an attorney or consulting with one in your area so you at least can get some kind of idea how to proceed.
No, sending child support to CSE is not considered contact with the child in TX. He's not writing, phoning or coming to see her, so just sending money to an office is not contact.
You can find statutes relating to the TPR and adoption at this link. Scroll down to Title 5 under Chapters 161 and 162.
http://www.capitol.state.tx.us/statutes/fa.toc.htm
Some grounds to file under..
FAMILY CODE
CHAPTER 161. TERMINATION OF THE PARENT-CHILD RELATIONSHIP
SUBCHAPTER A. GROUNDS
§ 161.001. INVOLUNTARY TERMINATION OF PARENT-CHILD
RELATIONSHIP. The court may order termination of the parent-child
relationship if the court finds by clear and convincing evidence:
(1) that the parent has:
(A) voluntarily left the child alone or in the
possession of another not the parent and expressed an intent not to
return;
(B) voluntarily left the child alone or in the
possession of another not the parent without expressing an intent
to return, without providing for the adequate support of the child,
and remained away for a period of at least three months;
(C) voluntarily left the child alone or in the
possession of another without providing adequate support of the
child and remained away for a period of at least six months;
(F) failed to support the child in accordance
with the parent's ability during a period of one year ending within
six months of the date of the filing of the petition;
§ 161.005. TERMINATION WHEN PARENT IS
PETITIONER. (a) A parent may file a suit for termination of the
petitioner's parent-child relationship. The court may order
termination if termination is in the best interest of the child
§ 161.206. ORDER TERMINATING PARENTAL RIGHTS. (a) If
the court finds by clear and convincing evidence grounds for
termination of the parent-child relationship, it shall render an
order terminating the parent-child relationship.
(b) Except as provided by Section 161.2061, an order
terminating the parent-child relationship divests the parent and
the child of all legal rights and duties with respect to each other,
except that the child retains the right to inherit from and through
the parent unless the court otherwise provides.
(c) Nothing in this chapter precludes or affects the rights
of a biological or adoptive maternal or paternal grandparent to
reasonable access under Chapter 153.
§ 161.2061. TERMS REGARDING LIMITED POST-TERMINATION
CONTACT. (a) If the court finds it to be in the best interest of
the child, the court may provide in an order terminating the
parent-child relationship that the biological parent who filed an
affidavit of voluntary relinquishment of parental rights under
Section 161.103 shall have limited post-termination contact with
the child as provided by Subsection (b) on the agreement of the
biological parent and the Department of Protective and Regulatory
Services.
(b) The order of termination may include terms that allow
the biological parent to:
(1) receive specified information regarding the
child;
(2) provide written communications to the child; and
(3) have limited access to the child.
(c) The terms of an order of termination regarding limited
post-termination contact may be enforced only if the party seeking
enforcement pleads and proves that, before filing the motion for
enforcement, the party attempted in good faith to resolve the
disputed matters through mediation.
(d) The terms of an order of termination under this section
are not enforceable by contempt.
(e) The terms of an order of termination regarding limited
post-termination contact may not be modified.
(f) An order under this section does not:
(1) affect the finality of a termination order; or
(2) grant standing to a parent whose parental rights
have been terminated to file any action under this title other than
a motion to enforce the terms regarding limited post-termination
contact until the court renders a subsequent adoption order with
respect to the child.
§ 161.2062. PROVISION FOR LIMITED CONTACT BETWEEN
BIOLOGICAL PARENT AND CHILD. (a) An order terminating the
parent-child relationship may not require that a subsequent
adoption order include terms regarding limited post-termination
contact between the child and a biological parent.
(b) The inclusion of a requirement for post-termination
contact described by Subsection (a) in a termination order does
not:
(1) affect the finality of a termination or subsequent
adoption order; or
(2) grant standing to a parent whose parental rights
have been terminated to file any action under this title after the
court renders a subsequent adoption order with respect to the
child.
§ 161.101. PETITION ALLEGATIONS. A petition for the
termination of the parent-child relationship is sufficient without
the necessity of specifying the underlying facts if the petition
alleges in the statutory language the ground for the termination
and that termination is in the best interest of the child.
§ 162.001. WHO MAY ADOPT AND BE ADOPTED. (a) Subject
to the requirements for standing to sue in Chapter 102, an adult may
petition to adopt a child who may be adopted.
(b) A child residing in this state may be adopted if:
(1) the parent-child relationship as to each living
parent of the child has been terminated or a suit for termination is
joined with the suit for adoption;
(2) the parent whose rights have not been terminated
is presently the spouse of the petitioner and the proceeding is for
a stepparent adoption;
(3) the child is at least two years old, the
parent-child relationship has been terminated with respect to one
parent, the person seeking the adoption has been a managing
conservator or has had actual care, possession, and control of the
child for a period of six months preceding the adoption or is the
child's former stepparent, and the nonterminated parent consents to
the adoption; or
§ 162.002. PREREQUISITES TO PETITION. (a) If a
petitioner is married, both spouses must join in the petition for
adoption.
(b) A petition in a suit for adoption or a suit for
appointment of a nonparent managing conservator with authority to
consent to adoption of a child must include:
(1) a verified allegation that there has been
compliance with Subchapter B ; or
(2) if there has not been compliance with Subchapter
B, a verified statement of the particular reasons for
noncompliance.
§ 162.003. PRE-ADOPTIVE HOME SCREENING AND
POST-PLACEMENT REPORT. In a suit for adoption, a pre-adoptive home
screening and post-placement report must be conducted as provided
in Chapter 107.
Added by Acts 1995, 74th Leg., ch. 20, § 1, eff. April 20, 1995.
Amended by Acts 1995, 74th Leg., ch. 751, § 73, eff. Sept. 1,
1995; Acts 1995, 74th Leg., ch. 800, § 1, eff. Sept. 1, 1995;
Acts 2001, 77th Leg., ch. 133, § 6, eff. Sept. 1, 2001.
§ 162.0045. PREFERENTIAL SETTING. The court shall
grant a motion for a preferential setting for a final hearing on an
adoption and shall give precedence to that hearing over all other
civil cases not given preference by other law if the social study
has been filed and the criminal history for the person seeking to
adopt the child has been obtained.
§ 162.009. RESIDENCE WITH PETITIONER. (a) The court
may not grant an adoption until the child has resided with the
petitioner for not less than six months.
(b) On request of the petitioner, the court may waive the
residence requirement if the waiver is in the best interest of the
child.