Actually, these lists do not prove apostolic succession. These are lists of following patriarchs, but in most cases predecessors couldn't ordain their successors since they had died prior to their successor's enthonements. There are no lists proving apostolic succession since 3 bishops are needed for ordination and after a few generations such lists will be impossible to be read.
They are nice but they do not answer op's question.
I agree. The lists of patriarchs also have the issue that, in some cases, there are gaps (e.g., vacancy of see for a long period of time, rival claimants, war). But I would go on to say that even the OP's question seems unclear. "Apostolic succession" for the Orthodox means more than just the continuity of laying on of hands in ordination going back in an unbroken chain to the apostles, though that is obviously an important part of it. Many Churches can have this "physical" unbroken succession while being cut off from "apostolic succession". For instance, RC's accept the succession of the Orthodox but not of the Anglicans, despite both having maintained this form of "apostolic succession".
If I'm not mistaken, when a bishop is ordained, records are kept of who was ordained by whom when and where. Since a minimum of two or three bishops are required for ordination of another bishop(s), that's quite a "tree" of records to go through (as Michal said), but I suppose it could be done. The real issue is what to do when you run out of records. Their absence doesn't mean that they never existed, but stuff happens and we lose stuff. Then what? That doesn't call the physical succession into question anymore than the lack of autographs of the Scriptural books means that they aren't authentic. The idea of Tradition (and apostolic succession would certainly fall under this) as the "living memory of the Church" means that the Church can vouch for authenticity even when a record can't be found to do so.
The need for "lists" is really more of an issue for those groups of recent and questionable origin who want to assert the authority of antiquity. I've seen such lists online, tracing ordinations back to multiple lines (e.g., a line going back to some random Oriental bishops, another line going back to Pope Pius V, etc.), but even those lists stop at a certain point for lack of records or lack of trying (presumably believing that after a certain point they've made their point and need not push it anymore). No "apostolic" Church (and by this I mean not only OO, but also EO, RC, and let's throw in Anglicans for good measure since they seem to have retained a physical succession) fusses too much over maintaining a meticulous database of their physical successions: they keep records as best they can, but they simply do what they do because that's what Church does.