I think that the seeds of the big showy oriental poppies are usually sterile, but I may be wrong. Other poppies will grow easily from seed and indeed will seed themselves around the garden.

As ojib says - depends on the poppies you have. I have found most poppies self seed, popping up everywhere in the flower bed. The large red perrenial flamboyant poppies are best dug up/split and replanted - every bit of tuber of these will produce a plant and flower ... even broken off bits.

I have read that Butterflies wont go into a garden where there are Poppies, so have always pulled them up.

They are certainly loved by bees, and I believe van gough did paint about poppies and butterflies. Perhaps, our resident artist, Noseypotter, knows more about the connection?!!

I have masses of poppies, all different kinds, and I also have masses of butterflies so I think you could leave some to grow Diane.

I know that the butterflies here love Iceland Poppies.