Using the Triangle To Quad option on this mesh produces a bunch of disconnected triangles, like in the photo.
What is the easiest way to remove these so that they are replaced by quads?
From that exact view (all those exact faces selected):
EDIT:
Mr Zak's suggestion to use Grid Fill greatly improves this answer by reducing the last three steps to just one:
Ctrl
+F
> Grid Fill. In a more complicated case, it can be done by hand, filling Ngon and cutting it withJ
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