Why only half of Brebeuf's skull is at the Midland Shrine
From a Homily of Most Reverend Terrence Prendergast, S.J.:
The "Blackrobes" finally gave up their grand project, burned Ste-Marie to the ground and, after one more terrible winter on nearby Christian Island, returned by canoe to Quebec. They carried with them Brébeuf's skull, which they eventually handed over to the Ursuline nuns for safekeeping, and the Jesuits left Canada entirely shortly after the arrival of the British.
They did not return until 1840, by which time the Ursulines felt the revered skull was theirs by law of possession. A literal saw-off was reached, and explains why, today, half of Brébeuf's skull lies in the shrine and half remains with the nuns.