If you are a cardinal, does that mean that you are an immediate successor to a dead or resigned pope? Being a cardinal means that you are one of the "Princes of the Catholic Church". If a pope resigned or died while in reign, the College of Cardinals is in-charged of the Catholic Church during the Sede Vacante period. If you are a cardinal during that time, are you an acting pope or the College of Cardinals is leaidng the Church as one and not divided group?
During the Sede Vacante period the College of Cardinals have no real powers and thus can not be the immediate successor(s) of a pope, but simply maintain that the everyday affairs are kept going. At the moment of a pontiffs death all cardinals who are head of a dicastery loose their positions until the election of a new pope, at which time the new pontiff may or may not return them to their former positions. 

The cardinals simply maintain that things move along as they should. 


  THE POWERS OF THE COLLEGE OF CARDINALS DURING THE VACANCY OF THE APOSTOLIC SEE 
  
  
  During the vacancy of the Apostolic See, the College of Cardinals has no power or jurisdiction in matters which pertain to the Supreme Pontiff during his lifetime or in the exercise of his office; such matters are to be reserved completely and exclusively to the future Pope. I therefore declare null and void any act of power or jurisdiction pertaining to the Roman Pontiff during his lifetime or in the exercise of his office which the College of Cardinals might see fit to exercise, beyond the limits expressly permitted in this Constitution. 
  During the vacancy of the Apostolic See, the government of the Church is entrusted to the College of Cardinals solely for the dispatch of ordinary business and of matters which cannot be postponed (cf. No. 6), and for the preparation of everything necessary for the election of the new Pope. This task must be carried out in the ways and within the limits set down by this Constitution: consequently, those matters are to be absolutely excluded which, whether by law or by practice, come under the power of the Roman Pontiff alone or concern the norms for the election of the new Pope laid down in the present Constitution. 
  I further establish that the College of Cardinals may make no dispositions whatsoever concerning the rights of the Apostolic See and of the Roman Church, much less allow any of these rights to lapse, either directly or indirectly, even though it be to resolve disputes or to prosecute actions perpetrated against these same rights after the death or valid resignation of the Pope.12 All the Cardinals are obliged to defend these rights. 
  During the vacancy of the Apostolic See, laws issued by the Roman Pontiffs can in no way be corrected or modified, nor can anything be added or subtracted, nor a dispensation be given even from a part of them, especially with regard to the procedures governing the election of the Supreme Pontiff. Indeed, should anything be done or even attempted against this prescription, by my supreme authority I declare it null and void. 
  Should doubts arise concerning the prescriptions contained in this Constitution, or concerning the manner of putting them into effect, I decree that all power of issuing a judgment in this regard belongs to the College of Cardinals, to which I grant the faculty of interpreting doubtful or controverted points. I also establish that should it be necessary to discuss these or other similar questions, except the act of election, it suffices that the majority of the Cardinals present should concur in the same opinion. 
  In the same way, should there be a problem which, in the view of the majority of the assembled Cardinals, cannot be postponed until another time, the College of Cardinals may act according to the majority opinion. - UNIVERSI DOMINICI GREGIS