apostolica sedes vacans: who’s in charge?

During the Vacancy of the Apostolic See, virtually everything in Rome stops.
The College of Cardinals will assemble in a General Congregation to start the process of governing in the transition. Of course, they will see to the proper mourning of Pope John Paul II and to the election of his successor. They will also see to the normal day-to-day operation of the Vatican, except in all things related to the Pontiff or his office. That is, if something comes up that cannot wait and it does not pertain to something derived from the powers of the pope, they can see to it.
During the first meeting of General Congregation, all cardinals are to make the following oath:

We, the Cardinals of Holy Roman Church, of the Order of Bishops, of Priests and of Deacons, promise, pledge and swear, as a body and individually, to observe exactly and faithfully all the norms contained in the Apostolic Constitution Universi Dominici Gregis of the Supreme Pontiff John Paul II, and to maintain rigorous secrecy with regard to all matters in any way related to the election of the Roman Pontiff or those which, by their very nature, during the vacancy of the Apostolic See, call for the same secrecy.
Next, each Cardinal shall add: “And I, N. Cardinal N., so promise, pledge and swear.” And, placing his hand on the Gospels, he will add: “So help me God and these Holy Gospels which I now touch with my hand.”

Joseph Cardinal Ratzinger, as the Dean of the College of Cardinals, is to precide over the General Congregation. The Congregation will meet daily starting on Monday until the Conclave begins. This is to allow the Camerlengo, Eduardo Cardinal Martínez Somalo, to hear the opinions of the College of Cardinals and for him to communicate whatever is needed.
Who is the Camerlengo? He is the Chamberlain of the Apostolic Chamber and only one of two Cardinals to retain their duties. The Apostolic Constitution Pastor Bonus describes his duties:

When the Apostolic See falls vacant, it is the right and the duty of the cardinal camerlengo of the Holy Roman Church, personally or through his delegate, to request reports from all the administrations dependent on the Holy See on their patrimonial and economic status as well as information on any extraordinary business that may at that time be under way, and, from the Prefecture for the Economic Affairs of the Holy See he shall request a financial statement on income and expenditures of the previous year and the budgetary estimates for the following year. He is obliged to submit these reports and estimates to the College of Cardinals.

He is also the person who officially and formally confirms and certifies the Pope’s death.
The other Cardinal retaining power, as mentioned previously, is the Major Penitentiary, James Francis Cardinal Stafford. This tribunal’s function is one directly having to do with the well-being of souls and therefore cannot be completely limited during the vacancy. If an emergency appeal for the absolution of an excommunication, indult, censure, etc, came to Rome, it is the Penitentiary’s duty to hear of the request. As these proceedings are kept under the seal of the confessional, no one can really give an example of such a situation. My best guess is someone who is under excommunication is ill- and the fear of death exists- repents and asks to be rejoined to the faithful, the request will go to this office, assuming the excommunication is reserved to the Holy See. Such examples of this would be a priest who broke the seal of confession or someone who takes the Body of Christ in the sacramental form and throws it away or retains it for sacrilegious purposs.
There are various other offices that remain open in some form: the Substitute of the Secretariat of State, the Secretary for Relations with States and the Secretaries of the Dicasteries of the Roman Curia. Again, none of their actions are derived from the Pontiff and they are governed by the College of Cardinals until a new pope is elected. The secretaries manage the business and human resources of the Roman Curial offices. The Almoner of His Holiness is the person designated to coordinate works of charity in line with the Pope’s directives. He is to continue to coordinate these works, subject to the College, until the election of a new Pope.
All civil powers of the Pope (as head of state of the Vatican City State) now fall to the College of Cardinals. They may not issue decrees unless it is urgent and they are only effective until the election of a new pope. He may then decide to confirm the decrees.
Lastly, the various tribunals of the Holy See, such as the Roman Rota, can still hear cases as normal.
For the general faithful, there should usually be no effect felt by the Curial offices closing. The local Church still operates as it always does.