Place the carnitas in a slow cooker. Add 1 cup of water, and cook on low heat for 6 to 8 hours.
When the carnitas are finished cooking, remove the meat to a cutting board and shred it apart.
To assemble the burritos: Warm the tortillas in the oven and place on a large cutting board. Divide the filling ingredients between the tortillas, then wrap the tortillas into burritos. Serve immediately with lime wedges.