The College of Cardinals serves a caretaker rule, but doesn't exercise the full rights of a Papal head of state.
After the death or resignation of a pope, the Holy See enters a period
of sede vacante. In this case the particular church is the Diocese of
Rome and the "vacant seat" is the cathedra of Saint John Lateran, the
cathedral church of the Bishop of Rome. During this period, the Holy
See is administered by a regency of the College of Cardinals.
According to Universi Dominici gregis, the government of the Holy See
and the administration of the Catholic Church during sede vacante
falls to the College of Cardinals, but in a very limited capacity. At
the same time, all the heads of the departments of the Roman Curia
"cease to exercise" their offices. The exceptions are the Cardinal
Camerlengo, who is charged with managing the property of the Holy See,
and the Major Penitentiary, who continues to exercise his normal role.
If either has to do something which normally requires the assent of
the Pope, he has to submit it to the College of Cardinals. Papal
legates continue to exercise their diplomatic roles overseas, and both
the Vicar General of Rome and the Vicar General for the Vatican City
State continue to exercise their pastoral role during this period. The
postal administration of the Vatican City State prepares and issues
special postage stamps for use during this particular period, known as
"sede vacante stamps".