Does Rebirth Make Sense? http://www.accesstoinsight.org/lib/authors/bodhi/bps-essay_46.html
The channel for the transmission of kammic influence from life to life across the sequence of rebirths is the individual stream of consciousness. Consciousness embraces both phases of our being — that in which we generate fresh kamma and that in which we reap the fruits of old kamma — and thus in the process of rebirth, consciousness bridges the old and new existences. Consciousness is not a single transmigrating entity, a self or soul, but a stream of evanescent acts of consciousness, each of which arises, briefly subsists, and then passes away. This entire stream, however, though made up of evanescent units, is fused into a unified whole by the causal relations obtaining between all the occasions of consciousness in any individual continuum. At a deep level, each occasion of consciousness inherits from its predecessor the entire kammic legacy of that particular stream; in perishing, it in turn passes that content on to its successor, augmented by its own novel contribution. Thus our volitional deeds do not exhaust their full potential in their immediately visible effects. Every volitional deed that we perform, when it passes, leaves behind a subtle imprint stamped upon the onward-flowing stream of consciousness. The deed deposits in the stream of consciousness a seed capable of bearing fruit, of producing a result that matches the ethical quality of the deed.
When we encounter suitable external conditions, the kammic seeds deposited in our mental continuum rise up from their dormant condition and produce their fruits. The most important function performed by kamma is to generate rebirth into an appropriate realm, a realm that provides a field for it to unfold its stored potentials. The bridge between the old existence and the new is, as we said above, the evolving stream of consciousness. It is within this stream of consciousness that the kamma has been created through the exercise of volition; it is this same stream of consciousness, flowing on, that carries the kammic energies into the new existence; and it is again this same stream of consciousness that experiences the fruit. Conceivably, at the deepest level all the individual streams of consciousness are integrated into a single all-embracing matrix, so that, beneath the surface of events, the separate kammic accumulations of all living beings crisscross, overlap, and merge. This hypothesis — though speculative — would help account for the strange coincidences we sometimes meet that prick holes in our assumptions of rational order.
The generative function of kamma in the production of new existence is described by the Buddha in a short but pithy sutta preserved in the Anguttara Nikaya (AN III.76). Venerable Ananda approaches the Master and says, "'Existence, existence' is spoken of, venerable sir. In what way is there existence?" The Buddha replies: "If there were no kamma ripening in the sensory realm, no sense-sphere existence would be discerned. If there where no kamma ripening in the form realm, no form-sphere existence would be discerned. If there were no kamma ripening in the formless realm, no formless-sphere existence would be discerned. Therefore, Ananda, kamma is the field, consciousness the seed, and craving the moisture for beings obstructed by ignorance and fettered by craving to be established in a new realm of existence, either low (sense-sphere), middling (form-sphere), or high (formless-sphere)."