I was very very concerned about removing my papers before the whole quilt was assembled. But based on advice from this quilt after the first two rows of flowers were sewn together I started removing papers. Always leave one row of papers where you will be attaching additional hexigons. The hexi's held their shape just fine without the papers and having the fabric flexible as the quilt got larger made adding to it much easier.
So in short - remove all the papers except on the edge where you will be attaching additional flowers or hexis.