When the Pope…the leader of the Roman Catholic Church…dies, they, of course, have a funeral, and go into a Conclave where they pursue the task of electing a new pope.
This could take days, if not weeks.
Neither nations nor corporations shut down when their respective leaders transition.
There is no such thing as a “Vice Pope” to temporarily step in.
So…who calls the shots and runs the show?
The College of Cardinals?
Yes
But it is really administered by the Camerlengo but the College of Cardinals fulfill the role of giving the papal approval as needed.
The Chamberlain (Camerlengo) and Dean of the College of Cardinals are the important ones.
Cardinal Kevin Farrell, an Irish-American, is the Camerlengo currently.
The Dean basically organizes and runs the election of the new Pope.
My understanding is that there are certain actions which only the Pope can do, such as elevating priests to the rank of bishop, issuing official statements of church policy, and excommunicating people. Everything else can (and usually is) done by members of the Holy See, and those things that only a Pope can do aren’t typically so time-sensitive that they can’t wait for a few months.
You don’t need a pope for that; as a matter of fact, people can excommunicate themselves. Canon law has the notion of “latae sententiae” crimes, meaning crimes that trigger their sentence automatically, without the need for a court to pronounce it. If you commit apostasy or heresy, attack the pope physically, or procure an abortion, then that will excommunicate you latae sententiae.
And as for making priests bishops: For this, you need to distinguish two acts. One is the consecration of a bishop, i.e., conferring the sacrament that turns a non-bishop into a bishop. There’s nothing particularly papal about this; any bishop can consecrate another bishop (of course the pope can, too, because the pope is also a bishop, but he doesn’t have a monopoly on this).
The other act is the administrative appointment of a person to the position of bishop of a particular diocese. This is something which, under Canon law, requires the approval of the Holy See, but I’m fairly certain that the camerlengo can appoint bishops to vacant dioceses during a sede vacante.
But not cardinals, right? You wouldn’t want the camerlengo to be able to pack the college of cardinals just before the election.
I have to correct myself here, apparently neither the camerlengo nor the college of cardinals as a whole can appoint a bishop sede vacante - a vacant diocese would be run by a temporary administrator for the time being (who may well be a bishop in the sense of having been ordained as one in the past, e.g. as an auxiliary bishop - but he wouldn’t be ordinary bishop of this diocese). Appointing cardinals would also be out of the question then.
Canon law is a fascinating thing. Another peculiarity of it is the possibility for a pope to appoint cardinals “in pectore”. In essence, the appointment is a secret: The pope makes the appointment but doesn’t tell anyone about it. Later, when the pope dies or changes his mind, the appointment becomes public, and the appointee is then considered a cardinal retroactively, from the time of the secret appointment.
So we “recovered Catholic” atheists are de facto excommunicated? Cool, more resume material. Or is there still some administrative procedure that needs to happen?
Key to the plot of the movie Conclave. Is there really no record? What’s to prevent some rando showing up claiming to be a Cardinal? How often has an in pectore appointment happened?
The Catholic Encyclopedia says that the pope has to publish the appointment before he dies:
Until they have been publicly announced these cardinals acquire no rights, and if the pope dies before having declared their names they do not become members of the Sacred College;
Yup. Repudiating the Catholic faith is, from the perspective of canon law, apostasy, which carries a lata sententiae excommunication according to canon 1364 (“canon” is the name for the individual sections in the Code of Canon Law). But note that excommunication does not mean (from the perspective of the church) that your membership in the church ends; baptism is a sacrament that cannot be undone, so a baptised person will always remain a member of the church - it only means you’re ineligible to receive sacraments. It can be undone if you repent and an official of the church (usually the ordinary, i.e. the bishop of the local diocese) absolves you. In fact, under canon law you’re entitled to have your excommunication lifted if your repentance is genuine.
Does that mean, in effect, that excommunication doesn’t make the person not a Catholic; it just means in effect its literal sense, that they can’t take Communion? – or maybe are also not eligible for other rites of the Catholic Church?
Excommunication means you remain a baptised Catholic, but you’re unable to receive sacraments or have any type of ecclesiastical office until the excommunication is lifted. This includes the Eucharist, but it also includes other sacraments, such as marriage. But note that bishops have power to grant exemptions (“dispensations”). This is actually quite common in Germany: The German government maintains an official register of people’s religious denomination for tax purposes because church members pay an extra tax to the church that’s levied by the government. You can opt out from this tax by declaring at a local government office that you’re dissociating yourself from the church, and hundreds of thousands of people do this every year, but the Catholic bishops in Germany argue that this constitutes apostasy and hence latae sententiae excommunication. I myself did this several years ago, but my girlfriend is a practising Catholic and will insist on a church wedding if/when we get married. For this purpose I’ll need to obtain a dispensation from the local bishop. My understanding is that this is usually granted in such situations.
The most common hangup for American Catholics is getting divorced and then wanting to remarry as a Catholic. First they need to receive an official annulment from their local diocese, then reinstate themselves with the church. Some local panels are pretty loose about it, but others have a history of being notoriously stingy in granting them.
Some Catholic schools have been known to refuse to admit children whose parent has been excommunicated. Oddly enough, they usually accept non-Catholic children as long as their parents agree to let them go through the standard religion classes (and not make waves.)
Thanks for explanations, both of you.
This was done mainly in Communist or Muslin countries, where the appointee would have been in danger if the government found out about it.
Do they have canvas skies hanging over the trees? 
I assume you are referring to parents who remarried after a divorce without an annulment. Divorce doesn’t result in excommunication and even remarrying civilly after a divorce doesn’t result in excommunication . “Excommunication” doesn’t simply mean you can’t receive Communion - a Catholic is supposed to be in a state of grace to receive Communion, and generally speaking, people who remarry without an annulment are not. In exactly the same way that anyone else who has committed a mortal sin and not received absolution is not supposed to receive communion. There’s a list of specific sins that result in excommunication (either automatic or judicial) that includes procuring an abortion, or breaking the seal of the confessional.
But how would the school even know if a parent was divorced and remarried? I’ve never heard of a Catholic school that required the parents’ marriage documents to register a child.
In the olde days, when Catholic schools were stuffed with Baby Boomers, one of the questions they asked parents when enrolling a child was, “are you in good standing with the Church?” and what parish you belonged to.
Whether they continue to ask that question now that they’re more flexible about admitting children from non-Catholic homes I don’t know.
They did ask those questions back then - but even then , remarriage after a divorce didn’t result in excommunication. Of course, it also almost never happened back then.