Paint Roller is Shedding

[Tony Thompson]

I've been painting cielings with kilz and have noticed the roller is leaving shreds of material all over the cieling. I've noticed this in offices and other houses too; both on walls and ceilings.

Does the quality of the roller need to be better or the quality of the paint? I also painted some walls with mid-grade sherwin williams and have noticed some shredding. Whats the secret to a smooth coat of paint with no shreds? :D