I want to understand the technicality of rebirth and what happens to conditioned self

Correct me if I'm wrong about my current understanding of Buddhism: There is no eternal self or essence in me, but I am just a conditioned-self, an illusion created by the interaction of the five aggregates. Each time I do something, or will something, its this distorted conditioned-self in play, right? Now, I want to understand what happens to this conditioned self when we die. You say its just an *illusion*, but lets take a practical example: A person dies in New York, and then is being reborn in Washington D.C the next moment. So here, you want to say the conditioned-self (illusion) travelled all the way from New York to D.C. to affect his/her next birth? As a corollary to this question, I would also like to understand the technicality of kamma. Say a person violates the precept of non-killing in New York in his/her present birth. How does the kamma know whom to punish 50 years later when that same person is reborn in D.C.? (You may say here that there is no external law-maker, but kamma is just in our minds. But that's still begging the question - *How does it know whom to punish 50 years later?*)