I do lots of paper piecing- my favorite technique! I always leave the paper on until the blocks are sewn together- when there is no more sewing to be done to a block then I might remove paper- but often I just sit down & remove them all after the top is together- that way all of the seams are secured- everything is stable and it's time to sit down with the top & remove them- I shorten my stitch length (on my machine I use a 1.5) then I hold the seam and tear the paper away like tearing on dotted lines.
if you have not paper pieced before visit Carol Doak's web site- she is considered the 'queen of paper piecing' (or the pioneer) has many hints, tips, helps and free blocks to try out & learn the technique before jumping into something advanced. it will be well worth your time in the long run to go there & do a couple practice blocks first- you could always turn them into placemats, table runners (or a whole quilt)