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In the Latin Church of the Catholic Church, the ordinary minister of baptism is a bishop, priest, or deacon (canon 861 §1 of the Code of Canon Law), and in normal circumstances, only the parish priest of the person to be baptized, or someone authorized by the parish priest may do so licitly (canon 530). "If the ordinary minister is absent or impeded, a catechist or some other person deputed to this office by the local Ordinary, may lawfully confer baptism; indeed, in a case of necessity, any person who has the requisite intention may do so (canon 861 §2), even a non-Catholic or indeed a non-Christian.
By "a case of necessity" is principally meant imminent danger of death because of either illness or an external threat. "The requisite intention" is, at the minimum level, the intention "to do what the Church does" through the rite of baptism.
In the Eastern Catholic Churches, a deacon is not considered an ordinary minister. Administration of the sacrament is reserved, as in the Latin Church, to the parish priest. But, "in case of necessity, baptism can be administered by a deacon or, in his absence or if he is impeded, by another cleric, a member of an institute of consecrated life, or by any other Christian faithful; even by the mother or father, if another person is not available who knows how to baptize" (canon 677 of the Code of Canons of the Eastern Churches.)
The discipline of the Eastern Orthodox Church, Oriental Orthodoxy and the Assyrian Church of the East is similar to that of the Eastern Catholic Churches. They require the baptizer, even in cases of necessity, to be of their own faith, on the grounds that a person cannot convey what he himself does not possess, in this case membership in the Church. The Latin Church does not insist on this condition, considering that the effect of the sacrament is not produced by the person who baptizes, but by the Holy Spirit.
Episcopal Church and others
For the Episcopal Church in the United States of America, the 1979 Book of Common Prayer states that "Holy Baptism is especially appropriate at the Easter Vigil, on the day of Pentecost, on All Saints' Day or the Sunday after All Saints' day, and on the Feast of the Baptism of our Lord . . . It is recommended that, as far as possible, Baptisms be reserved for these occasions or when a bishop is present. If on any one of the above-named days the ministry of a bishop or priest cannot be obtained, the bishop may specially authorize a deacon to preside. In that case, the deacon omits the prayer over the candidates, page 308, and the formula and action which follow." The Book of Common Prayer also specifies under the heading "Emergency Baptism" the following:
"In case of emergency, any baptized person may administer Baptism according to the following form. Using the given name of the one baptized (if known), pour water on him or her, saying
"I baptize you in the Name of the Father, and of the Son, and of the Holy Spirit.
"The Lord's Prayer is then said.
"Other prayers, such as the following, may be added
"Heavenly Father, we thank you that by water and the Holy Spirit you have bestowed on upon this your servant the forgiveness of sin and have raised him to the new life of grace. Strengthen him, O Lord, with your presence, enfold him in the arms of your mercy, and keep him safe forever.
"The person who administers emergency Baptism should inform the priest of the appropriate parish, so that the fact can be properly recorded.
"If the baptized person recovers, the Baptism should be recognized at a public celebration of the Sacrament with a bishop or priest presiding, and the person baptized under emergency conditions, together with the sponsors or godparents, taking part in everything except the administration of the water."
Similar provisions exist throughout the constituent churches of the Anglican Communion, of which the Episcopal Church in the United States of America is one.
Infants, babies and fetuses
The Roman Ritual declares that a child is not to be baptized while still enclosed (clausus) in its mother's womb, it supposes that the baptismal water cannot reach the body of the child. When, however, this seems possible, even with the aid of an instrument, Benedict XIV  declares that midwives should be instructed to confer conditional baptism. The Ritual further says that when the water can flow upon the head of the infant the sacrament is to be administered absolutely; but if it can be poured only on some other part of the body, baptism is indeed to be conferred, but it must be conditionally repeated in case the child survives its birth, It is to be noted that in these last two cases, the rubric of the Ritual supposes that the infant has partly emerged from the womb. For if the fetus was entirely enclosed, baptism is to be repeated conditionally in all cases.
In case of the death of the mother, the fetus is to be immediately extracted and baptized, should there be any life in it. Infants have been taken alive from the womb well after the mother's death. After the Cæsarean incision has been performed, the fetus may be conditionally baptized before extraction if possible; if the sacrament is administered after its removal from the womb the baptism is to be absolute, provided it is certain that life remains. If after extraction it is doubtful whether it be still alive, it is to be baptized under the condition: "If thou art alive". According to Catholic teaching, the fetus is animated by a human soul from the very beginning of its conception. In cases of delivery where the issue is a mass that is not certainly animated by human life, it is to be baptized conditionally: "If thou art a man." 
Controversial baptisms of Jews
In 1858, Edgardo Mortara, then six years old, was taken from his Jewish parents by the police of the Papal States. He had reportedly been baptized by a Roman Catholic servant girl of the family while he was ill, because she feared that otherwise he would not be saved if he died.
The Jewish orphans controversy is a legal dispute that occurred after the Second World War when the Holy See under Pope Pius XII issued instructions that Catholic institutions and families should keep baptized Jewish children in their ranks after they had been rescued from a likely deportation to Auschwitz.
A deathbed conversion is the adoption of a particular religious faith shortly before dying. Making a conversion on one's deathbed may reflect an immediate change of belief, a desire to formalize longer-term beliefs, or to complete a process of conversion already underway.
- Catholic Encyclopedia : baptism
- Syn. Diaec., vii, 5
- Lehmkuhl, n, 61