Advances in artificial procreation techniques have significantly changed Family Law, especially with regard to filiation, introducing substantial changes. The biological criterion, previously absolute, shares space with the criterion of affection in determining parenthood. The debiologization of paternity/maternity has meant that the status of filiation no longer depends exclusively on biological origin, opening space for other forms of civil kinship in addition to adoption. The 2002 Civil Code, by using the expression other origin in article 1.593, constituted a major advance in relation to the previous Civil Code of 1916. Although civil codification has advanced, contemplating filiation of other origin, there is a legislative gap with regard to assisted reproduction, especially to surrogate pregnancy. Interference in natural human processes with the aid of medical- scientific procedures creates problems, to the extent that the legal system is still constructed based on these natural facts, previously considered unchangeable. With the limited legislation, administrative and ethical standards issued by the CNJ and CFM, respectively, end up regulating the matter in practice, denouncing the vulnerability of legal relationships, in addition to often contributing to situations that are at odds with the ethical and legal principles imposed by the current system. The right to procreation as a fundamental right must be exercised responsibly, considering, mainly, the future child. The withdrawal of the parental project in a surrogate pregnancy after conception raises complex questions about the rights and responsibilities of those involved, as well as the impact on family relationships. The work is part of the area of Constitutional Civil Law, in the research line of Contemporary Civil Law Institutions, divided into three chapters, in addition to the introduction and the conclusion. The first chapter addresses the human reproduction technique of surrogate pregnancy, followed by the chapter that deals with filiation and, finally, the chapter that deals with the withdrawal/ of the authors of the parental project in the surrogate pregnancy.