The Catholic Church has always taught that the three valid forms of Baptism are immersion, pouring, and sprinkling. Evidence that the Church has validated the form of pouring instead of immersion is demonstrated by the Didache which was written around A.D. 70:
"Concerning baptism, baptize in this manner: Having said all these
things beforehand, baptize in the name of the Father and of the Son
and of the Holy Spirit in living water [that is, in running water, as
in a river]. If there is no living water, baptize in other water; and,
if you are not able to use cold water, use warm. If you have neither,
pour water three times upon the head in the name of the Father, Son,
and Holy Spirit."
These instructions were composed either while some of the apostles and disciples were still alive or during the next generation of Christians, and they represent an already established custom.
Perhaps the "minimum" amount of water required to effectively administer the sacrament is impossible to quantify. In order to answer the question as accurately as possible, lets assess which situation would call for the smallest amount.
These days, the rules for administering the Sacrament of Baptism are clearly given in the Rituale Romanum:
The form for baptism is as follows: I baptize you in the name of the
Father, and of the Son, and of the Holy Spirit, and it is absolutely
essential. In no circumstance can it be altered, and these words must
be pronounced simultaneously with the pouring of the water. The water
is to be poured on the head with a triple ablution (or the head is to
be immersed three times), each time in the form of a cross, saying the
The Rituale Romanum also decrees that in the event of a complicated birth an emergency conditional baptism should be administered to the infant:
No child is to be baptized while still enclosed in the mother's womb,
as long as there is a probable hope that it can be properly brought
forth and then baptized. If only the head of the child has come forth
and there is danger of its dying, it should be baptized on the head;
if afterward it is born and lives, baptism may not be repeated
conditionally. If another member of the body makes its appearance and
there is danger of death, the baptism should be conferred
conditionally upon that member; if the child lives after birth it must
be rebaptized conditionally. Should a mother die in confinement, the
fetus should be extracted by those obliged thereto by their
profession, and if there is a certainty that it lives, it should be
baptized absolutely, otherwise conditionally. A fetus baptized while
in the mother's womb must be rebaptized conditionally after birth.
One should see to it that every abortive fetus, no matter of what
period, be baptized absolutely if it is certainly alive. If there is
doubt about its being alive, it should be baptized conditionally.
Considering that a new born (or, unborn in the case of an abortion) infant/fetus is about as small as any recipient might be, I would say, "However much it takes to roll 3 beads of water across a baby's forehead.