The present invention provides auto-stopping CMP slurry compositions that minimize post-CMP non-uniformity and also extend the time that polishing can be continued beyond the end point without the risk of over-polishing the dielectric silicon dioxide film. Auto-stopping CMP slurry compositions according to the invention include ceria abrasive particles and an effective amount of a polyalkylamine such as polyethyleneimine dispersed in water. The methods of the invention include polishing a topographic dielectric silicon dioxide film layer using the auto-stopping CMP slurry compositions to obtain a dielectric silicon dioxide surface having a desired predetermined minimum step height.