Note: What follows is longer than the norm, and makes certain assumptions that could impact a large portion of the setting. Although this is not normal policy for the thread--usually a stated fact remains, no matter what--I'm willing, in this case, to field some discussion on this, and perhaps change if it enough people wish me to do so.
Line of Ascent: The precise means for a half-orc to ascend the Throne are as follows.
Within four years of taking the Throne, the current Emperor must select one of the Six Pillars from which his successor will come. This Pillar is known as the Presumptive from this point until a new Emperor ascends. This is the source of much of the political wrangling between Pillars, as they all seek the favor of the new Emperor.
Note that the Emperor cannot choose the Presumptive from which he (or she) came as the new Presumptive. He can choose the other Pillar from which he descends, though this is considered poor form unless he can justify his choice.
It is possible, although rare, for the Pillars to "veto" the Emperor's choice, but it requires a unanimous vote of all five Pillars (other than the Presumptive). The Emperor must then choose a different Pillar. This can occur only once; the Pillars cannot veto the Emperor's second choice. The majority of historical rejections occurred when an Emperor chose one of his own Pillars as Presumptive.
It is up to the Presumptive Pillar to decide which other Pillar it will join with to produce the next heir; this is the source of much more of the political wrangling, as each Pillar seeks the favor of the Presumptive.
An Emperor can change his mind after declaring a Presumptive, but only if he can give good reason to the Pillars, and only if at least three of the six Pillars vote to permit him to do so.