Short answer. No, not by agreement. Parental authority and responsibility may not be renounced or transferred except in the cases authorised by law, so a private arrangement handing a child to an aunt or a grandparent does not move the authority. The parents keep it, and keep the duties that come with it.

What the law says

Parental authority and responsibility may not be renounced or transferred except in the cases authorized by law.

Family Code, Article 210 — Parental Authority Cannot Be Renounced or Transferred. Read the full provision →

What the law says

In default of parents or a judicially appointed guardian, the following person shall exercise substitute parental authority over the child in the order indicated

Family Code, Article 216 — Order of Substitute Parental Authority. Read the full provision →

Authority over a child is not yours to give away

The rule is one sentence: parental authority and responsibility may not be renounced or transferred except in the cases authorized by law. It treats authority over a child as a duty attached to the parent rather than a right the parent owns, and duties cannot be signed over to whoever will take them. That is why the deed of waiver, the notarised letter and the affidavit handing custody to a relative do not do what families expect. They may record what everyone agreed, but they do not by themselves shift the authority, and the parent who signed one remains the parent in law.

The exceptions are statutory, not private

The article does allow transfer in the cases authorized by law, and those cases exist — but each of them is a route created by statute and travelled through a court, not a document the parties draft between themselves. The distinction is the whole point of the provision. If a family could move parental authority by consent, the protections the law builds around a child's upbringing would last exactly as long as the adults found them convenient. So the question is never whether everyone agreed; it is whether the law recognises the particular route taken.

What the relative caring for the child actually has

Substitute parental authority is a real thing, but it arises from the facts the law specifies rather than from the parents' choice. Article 216 provides that in default of parents or a judicially appointed guardian, the following person shall exercise substitute parental authority over the child in the order indicated, naming the surviving grandparent, then the oldest sibling over twenty-one and unfit or disqualified persons aside, then the child's actual custodian over twenty-one. Article 214 covers death, absence or unsuitability of the parents. Note the trigger in every case: the parents are gone or unable, not merely willing.

The practical problem this creates

A relative raising a child on a private arrangement runs into it at the school gate, the clinic and the passport counter, because the person with authority is elsewhere and may be uncooperative. The parent, meanwhile, has not shed the responsibility they thought they had transferred. Before signing anything, get clear on the facts that matter to the law: where each parent is, whether either is dead, absent or unsuitable, who has actually had the child and since when. Those facts, not the affidavit, determine which route is open.

Related provisions

Note. Statute text quoted on this page is reproduced from the official enactment and is linked to the full provision. The explanation around it is general legal information from Vivas & Nobles Law Office, not legal advice. Whether it applies to your situation depends on facts only a lawyer reviewing them can assess.