What happens to the five aggregates after death? What happens to the five skandhas of a particular person after death?


Do they stay together, and cause birth of a one specific person (which can be called rebirth), or do they separate?
If they separate, do they separate just into 5, or does each aggregate split into smaller parts?
If they separate, do they cause births of many different persons?


I'm interested in answers from many traditions, with references to relevant sources (scriptures, books, articles).

EDIT: I didn't get unambiguous answers to my questions, but what Suminda and Prahlad write seems to suggest that all the aggregates arise and pass all the time, but when we look at them at a higher level, we can conclude that four of the aggregates (sensation, perception, mental formations and consciousness) stay together and cause a new birth of one specific person, while the remaining aggregate (rūpa, matter) separates and splits into parts. Can anyone confirm/disconfirm this?

EDIT 2: I was asked to specify what is exactly meant by "overall structure of the aggregates remain intact", when we know that the aggregates arise and pass all the time. What I mean is the continuity of the illusion called "self". I have the illusion that I'm the same person as a moment ago, even though my body, my feelings, etc. have changed. Does this illusion continue after death? According to Buddhist doctrines, is there an illusion of the continuity of consciousness? Of the continuity of feelings? Of the continuity of the body?

I watched Yuttadhammo's video about rebirth and understood that Buddhists believe in perceived continuity of the consciousness after death. Is this a canonical opinion that can be concluded from Buddhist scriptures? How about the continuity of other aggregates?
1. Do they stay together, and cause birth of a one specific person (which can be called rebirth), or do they separate?

Even when you are alive, the 5 skandhas arise together in every experience. So when you ask "do they stay together", you are asking if the experience stays. No! The experience disappears immediately. There's no staying. The skandhas in this experience are not the same as the skandhas in the next. 

2. If they separate, do they separate just into 5, or does each aggregate split into smaller parts? 

The 5 skandhas are grouped into 2 categories. Nāma (mental) and Rūpa (physical). Rūpa contains only the 1st skanda and the Nāma contains the remaining 4.
Usually only Rūpa can arise independently, e.g.: a log, stone, corpse etc.
Nāma always needs to arise in association with Rūpa except in Arupa Brahma Realms. But again, when you ask "if they separate", you are making the assumption that there's something fixed lasting for a certain time period. It doesn't work that way. A single experience can contain a maximum of 17 thought moments. 1 Rūpa unit lasts only for 17 thought moments and there's no example in nature to compare to the time 1 thought moment lasts but to the lifespan of another thought moment.

The mind at the time of death


  When a person is about to die the bhavanga is interrupted, vibrates for one moment and passes away. The interruption is caused by an object which presents itself to the mind-door. As a result of this a mind-door-adverting citta arises. This is followed by five javana thought moments which are weak, lack reproductive power, and serve only to determine the nature of rebirth consciousness. The javanas may or may not be followed by two registering thought moments (tadaalambana). After this comes the death consciousness (cuti citta), which is identical in constitution and object to the bhava"nga citta. The cuti citta merely serves the function of signaling the end of life. It is important to appreciate the difference between the cuti citta and the javanas that precede it. The cuti citta is the end of the bhava"nga flow of an existence and does not determine the nature of rebirth. The javanas that occur just before the cuti citta arises form a kammic process and determine the nature of the rebirth consciousness.


3. If they separate, do they cause births of many different persons?

There's no separation. When a person dies, the Nāma doesn't appear in the body anymore. Only Rūpa caused due to reasons other than Nāma continue to appear. There's only one Patisandi citta. So the death of a being does not result in multiple births.


  we can conclude that four of the aggregates (sensation, perception,
  mental formations and consciousness) stay together and cause a new
  birth of one specific person, while the remaining aggregate (rūpa,
  matter) separates and splits into parts.


Again, there's no staying. They appear together and disappear instantly. Nāma does not go from this life to the next. The first citta of the next life is a result of the Javana cittas that occur just before the cuti citta.


  I have the illusion that I'm the same person as a moment ago, even
  though my body, my feelings, etc. have changed. Does this illusion
  continue after death?


Ignorance or Moha is a cetasika. The cetasikas are the mental factors or concomitants that arise and perish together with consciousness (citta), sharing its object and basis. Cetasikas don't appear independently from the cittas. So there's nothing going from this moment to the next. But that doesn't mean the next citta cannot have an ignorance cetasika.


  I watched Yuttadhammo's video about rebirth and understood that
  Buddhists believe in perceived continuity of the consciousness after
  death.


Venerable Yuttadhammo is talking about the continuity of experiencing. He's not implying a panchaskanda going from this life to the next or from this moment to the next.