What exactly is rebirth?

According to Buddhism, one's self is made of 5 aggregates.

The above is not accurate. According to Buddhism, one of the aggregates (sankhara aggregate) ignorantly assumes one or more of the 5 aggregates is a "self". Refer to SN 22.81.

But these agregagtes should dissolve at death

In Buddhism, the word "death" means the "death of a self-assumption" or "a being"; such as the "death of mother, father, sister, brother, self". As for the aggregates, they cease when life terminates or ends its time. But this is not called "death". "Death" ("marana") is the idea "a being" or "person" dies; which is the condition for sorrow, grief & suffering. Refer to SN 12.2.

So what links the new human B that is considered a reincarnation of human A ?

Nothing. Original Buddhism does not teach the above idea. In the original Pali suttas, there is no word that exactly means "reincarnation" or "rebirth".

As for the quote below (which is poorly translated), it means production of the assumption of various "beings" and "categories of beings". "A being" is merely a "view", "idea" and "state of clinging". Refer to SN 23.2 & SN 5.10.

"And what is birth? Whatever birth, taking birth, descent, coming-to-be, coming-forth, appearance of aggregates, & acquisition of [sense] spheres of the various beings in this or that group of beings, that is called birth. MN 141

In conclusion, the primary Pali word translated as "rebirth" is "upapajjati". "Upapajjati" means to "proceed", "walk" or "continue" in the same manner has a previous thing. This is contrasted with the word "paṭipajjati", which has the same suffix. "Paṭipajjati" means to walk in an opposite direction, such as walking the Path away from suffering and towards Nirvana. "Upapajjati" is to re-live or re-experience a previous experience. For example, if you commit an act of killing, the killing comes back to haunt the mind and the mind suffers from a similar trauma or violence that was previous inflicted when it engaged in killing. Therefore, due to violent killing, for example, a person takes "rebirth" in "hell". They proceed from one violent place (killing) to another violent place ("hell"). This is the meaning of "upapajjati"; which is commonly yet inaccurately translated as "rebirth".

Rebirth is a conventional truth. If, if you posit the wrong view of a permanent Self, then due to the ultimate emptiness of all phenomena, over all time, the space that is defined as 'I' must be empty. In other words, all intentional action by that 'I' must be balanced around '0'.

The only plausible link between spontaneous rebirths is that at all points of time, the All is still empty of permanent Self. From here there are two options:

1) Subject to the wrong view of Self, there is no pattern between rebirths. This also offers the overall '0' statistically, but goes against the regularity of experience, bringing in the spectre of chance and chaos.

2) Subject to the wrong view if Self, rebirths follow the laws of kamma-vipaka - during a life and in the spontaneous skip of rebirth - akin to Newton's third law of motion, but for intentional activity. This has continuity and regularity.

To me experience appears regular - even the laws of chance and chaos are definable laws.

But the Buddha stressed impermanence, and all this is intellectualism. He discouraged people from trying to figure out the exact workings of kamma, as the process is not fully decipherable, imo due to the fact that it is asking conventional truth to be superimposed onto ultimate truth, at least if Nagarjuna's take that 'there is not the slightest difference between Samsara and nibbana' is accepted.

Better concentrate on the here and now.

"According to Buddhism, one's self is made of 5 agregates.", maybe according to whom's ever Buddhism and Buddhists, but the Buddha did not told such. More: he repeatedly stressed out that ones own can not be found in the five aggregates.

As for what is birth:

"And what is birth? Whatever birth, taking birth, descent, coming-to-be, coming-forth, appearance of aggregates, & acquisition of [sense] spheres of the various beings in this or that group of beings, that is called birth. MN 141

And as part of the first Noble truth it's somehow pointless to call it "merely convention" since such would hinder one to take actions for a beyond. So for a serious practitioner it's very needed to avoid people who deny coming into being and the Noble Truths, people of grave wrong view.

What makes you the same person who wrote the question and now reading an answer? Desire? Not-knowing?

And without first things first, your practice becomes nothing but that of the many Jains around: a really poor living of real poor hypocriticals.

May you have an auspicious birth here, since it is the prerequisite of liberation.

(Note: not given for stacks, trade and exchange but as a tiny door out of the wheel of rebirth)

According to Buddhism there is nothing to be taken as a self, soul, I, me or mine. What is mistaken as a 'self' is a sequence of momentary experiences/actions/events occurring and ending one after the other. Each of these experiences has two aspects to it. The physical aspect and the mental aspect. The mental aspect is subdivided into 4 categories. Hence the five aggregates in total.

Each of these experiences are caused. None of them come to be without causes. One major cause of these experiences is Karma. It can be past karma or present Karma. Pleasant experiences are a result of good Karma and unpleasant experiences are a result of bad Karma.

'Living' simply means a session of these experiences/events arising and ending at a certain realm of existence. Dying simply means that the causes for arising of those experiences at that realm are no longer present or they have been overpowered by fresh causes. Near the end of each session, a fresh Karma comes forward to become the cause for the arising of the consciousness aggregate at another place where the supportive conditions are right for arising of a thought moment. Ex: at a womb after the reproductive union of male and female, a fertilized egg etc. Arising of this thought moment is the beginning of the next session of experiences. This is how the so called Life A is linked to Life B, human or otherwise.

In this framework there are only experiences and their causal relationships. Concepts like the 'brain' does not exist. So if you ask a question assuming that there is an entity called the brain existing within this framework, it will only lead to confusion and false views until you are ready to give up that assumption.