I disagree with both replies above, saying the Prayer of Exorcism can never be eliminated.
From the Rite of Baptism, Chapter V, “Rite of Baptism for Children in Danger of Death When No Priest or Deacon is Available”:
“163. If no one there is capable of directing the prayer, any member of the church may baptize, after reciting the Apostles’ Creed, by pouring water on the child while reciting the customary words (see no. 160, above). The creed may be omitted if necessary.
164. At the moment of death, it is sufficient for the minister to omit all other ceremonies and pour water on the child while saying the usual words (see no. 160, above). It is desirable that the minister, as far as possible, should use one or two witnesses.”
Do these “usual words” in n. 160 include the Prayer of Exorcism? Of course not. It has:
“160. Then the minister baptizes the child, saying:
N., I baptize you in the name of the Father,
The minister pours water upon the child.
and of the Son,
The minister pours water upon the child a second time.
and of the Holy Spirit.
The minister pours water upon the child a third time.”
(The Rites Volume One, Liturgical Press, 1990, ISBN: 0-8146-6015-0. page 434).
But according to the Introduction to the Rite of Baptism for Children:
“15. Baptism, whether for one child, or several, or even for a larger number, should be celebrated by the ordinary minister and with the full rite when there is no immediate danger of death.”
For adults the baptism ceremony normally does not include a Prayer of Exorcism. Normally there are separate ceremonies, the Scrutinies, at which there is a Prayer of Exorcism. But the normal ceremony of inititiation in the Rite of Christian Initation of Adults does not include a Prayer of Exorcism.