Here is what I've located under the Texas Family Code:
SUBCHAPTER D. VOLUNTARY ACKNOWLEDGMENT OF PATERNITY
§ 160.301. ACKNOWLEDGMENT OF PATERNITY. The mother of a
child and a man claiming to be the biological father of the child
may sign an acknowledgment of paternity with the intent to
establish the man's paternity.
Added by Acts 2001, 77th Leg., ch. 821, § 1.01, eff. June 14,
2001. Amended by Acts 2003, 78th Leg., ch. 1248, § 2, eff. Sept.
1, 2003.
§ 160.302. EXECUTION OF ACKNOWLEDGMENT OF
PATERNITY. (a) An acknowledgment of paternity must:
(1) be in a record;
(2) be signed, or otherwise authenticated, under
penalty of perjury by the mother and the man seeking to establish
paternity;
(3) state that the child whose paternity is being
acknowledged:
(A) does not have a presumed father or has a
presumed father whose full name is stated; and
(B) does not have another acknowledged or
adjudicated father;
(4) state whether there has been genetic testing and,
if so, that the acknowledging man's claim of paternity is
consistent with the results of the testing; and
(5) state that the signatories understand that the
acknowledgment is the equivalent of a judicial adjudication of the
paternity of the child and that a challenge to the acknowledgment is
permitted only under limited circumstances and is barred after four
years.
(b) An acknowledgment of paternity is void if it:
(1) states that another man is a presumed father of the
child, unless a denial of paternity signed or otherwise
authenticated by the presumed father is filed with the bureau of
vital statistics;
(2) states that another man is an acknowledged or
adjudicated father of the child; or
(3) falsely denies the existence of a presumed,
acknowledged, or adjudicated father of the child.
(c) A presumed father may sign or otherwise authenticate an
acknowledgment of paternity.
Added by Acts 2001, 77th Leg., ch. 821, § 1.01, eff. June 14,
2001.
§ 160.303. DENIAL OF PATERNITY. A presumed father of a
child may sign a denial of his paternity. The denial is valid only
if:
(1) an acknowledgment of paternity signed or otherwise
authenticated by another man is filed under Section 160.305;
(2) the denial is in a record and is signed or
otherwise authenticated under penalty of perjury; and
(3) the presumed father has not previously:
(A) acknowledged paternity of the child, unless
the previous acknowledgment has been rescinded under Section
160.307 or successfully challenged under Section 160.308; or
(B) been adjudicated to be the father of the
child.
Added by Acts 2001, 77th Leg., ch. 821, § 1.01, eff. June 14,
2001.
§ 160.304. RULES FOR ACKNOWLEDGMENT AND DENIAL OF
PATERNITY. (a) An acknowledgment of paternity and a denial of
paternity may be contained in a single document or in different
documents and may be filed separately or simultaneously. If the
acknowledgment and denial are both necessary, neither document is
valid until both documents are filed.
(b) An acknowledgment of paternity or a denial of paternity
may be signed before the birth of the child.
(c) Subject to Subsection (a), an acknowledgment of
paternity or denial of paternity takes effect on the date of the
birth of the child or the filing of the document with the bureau of
vital statistics, whichever occurs later.
(d) An acknowledgment of paternity or denial of paternity
signed by a minor is valid if it otherwise complies with this
chapter.
Added by Acts 2001, 77th Leg., ch. 821, § 1.01, eff. June 14,
2001.
§ 160.305. EFFECT OF ACKNOWLEDGMENT OR DENIAL OF
PATERNITY. (a) Except as provided by Sections 160.307 and
160.308, a valid acknowledgment of paternity filed with the bureau
of vital statistics is the equivalent of an adjudication of the
paternity of a child and confers on the acknowledged father all
rights and duties of a parent.
(b) Except as provided by Sections 160.307 and 160.308, a
valid denial of paternity filed with the bureau of vital statistics
in conjunction with a valid acknowledgment of paternity is the
equivalent of an adjudication of the nonpaternity of the presumed
father and discharges the presumed father from all rights and
duties of a parent.
Added by Acts 2001, 77th Leg., ch. 821, § 1.01, eff. June 14,
2001.
Ok now, here are some definitions provided by the Texas Code:
§ 101.0010. ACKNOWLEDGED FATHER. "Acknowledged father"
means a man who has established a father-child relationship under
Chapter 160.
Added by Acts 2001, 77th Leg., ch. 821, § 2.04, eff. June 14,
2001.
§ 101.0015. ALLEGED FATHER. (a) "Alleged father"
means a man who alleges himself to be, or is alleged to be, the
genetic father or a possible genetic father of a child, but whose
paternity has not been determined.
(b) The term does not include:
(1) a presumed father;
(2) a man whose parental rights have been terminated
or declared to not exist; or
(3) a male donor.
Added by Acts 2001, 77th Leg., ch. 821, § 2.04, eff. June 14,
2001.
Then here are the statutes regarding conservatorship and presumption of:
§ 153.131. PRESUMPTION THAT PARENT TO BE APPOINTED
MANAGING CONSERVATOR. (a) Subject to the prohibition in Section
153.004, unless the court finds that appointment of the parent or
parents would not be in the best interest of the child because the
appointment would significantly impair the child's physical health
or emotional development, a parent shall be appointed sole managing
conservator or both parents shall be appointed as joint managing
conservators of the child.
(b) It is a rebuttable presumption that the appointment of
the parents of a child as joint managing conservators is in the best
interest of the child. A finding of a history of family violence
involving the parents of a child removes the presumption under this
subsection.
Added by Acts 1995, 74th Leg., ch. 20, § 1, eff. April 20, 1995.
Amended by Acts 1995, 74th Leg., ch. 751, § 32, eff. Sept. 1,
1995; Acts 1997, 75th Leg., ch. 1193, § 20, eff. Sept. 1, 1997.
Since I'm not an attorney, I thought perhaps maybe someone here can interpret this. It sound to me like if paternity has been established, but there is no court order granting a particular party conservatorship or possessory, then it is presumed that they have joint conservatorship. Is this correct or not? I did not find anything in the code specifying that the mother has sole conservatorship unless a court order granting the father visitation exists. In Oklahoma, there is a specific statute that states such. Is this something that is implied in the Texas code?