Getting to the Baptism ritual itself:
18. In the celebration of the sacrament:
- The immediate preparation consists of:
- the solemn prayer of the celebrant, which, by invoking God and recalling his plan of salvation, blesses the water of baptism or makes reference to its earlier blessing;
- the renunciation of Satan on the part of parents and godparents and their profession of faith, to which is added the assent of the celebrant and the community; and the final interrogation of the parents and godparents.
- The sacrament itself consists of the washing in water by way of immersion or infusion, depending on local custom, and the invocation of the blessed Trinity.
The completion of the sacrament consists, first, of the anointing with chrism, which signifies the royal priesthood of the baptized and enrollment into the company of the people of God; then of the ceremonies of the white garment, lighted candle, and ephphetha rite (the last of which is optional).
The post-baptismal rites are seen as the “completion” of this first celebration. Most clergy I know omit the ephphetha (the unsealing of the ears and lips) but my current pastor utilizes it always.
19. Before the altar to prefigure the future sharing in the eucharist, the celebrant introduces and all recite the Lord’s Prayer, in which God’s children pray to their Father in heaven. Finally, a prayer of blessing is said over the mothers, fathers, and all present, to ask the outpouring of God’s grace upon them.
Even in parishes in which the font and altar are somewhat separated in the nave, my experience is that priests nearly always do this. Except when sheer numbers dictate otherwise.