Ulamog, the Infinite Gyre + Rite of Replication
You will shuffle your graveyard.
Rite of Replication creates a token “that's a copy of…” This is shorthand for creating a token whose base characteristics are those of the target. In particular, it's not a continuous effect.
When the token changes zones, its characteristics are still those of the object it's a copy of. Because that's not a continuous effect, there is no “tracking” problems when it changes zones (when an object changes zones, it becomes a new object, so effects affecting it in the previous zone typically don't affect it in the new one).
Since Ulamog's ability triggers from the graveyard (it's worded “when goes to the graveyard *from anywhere*”), and the token is still a copy of Ulamog in the graveyard, it will trigger. This is different from Clone copying Ulamog - in that case, because Clone is no longer Ulamog in the graveyard, you wouldn't shuffle.
Daniel Kitachewsky
L3, Paris, France
Rules NetRep