You must be talking about my yardYou can hardly make a mistake with Opuntias. I know of places where gardeners have dumped pruning cuttings and clippings. Over time, everything else is composted and gone except the opuntia pads, which grow, mutliply and become forests of plants with no help at all from man.
Buck has given advice that I'll agree with whole heartedly.
I usually pot my cuttings (pads) in a upright positon with about 1/3 to 1/2 of the pad in the soil medium so theres enough areoles in the soil to produce a good root system.
here's a few pictures of some new cuttings I'm rooting now to give an idea of the depth the pads are planted.
Legolas, I usually root single pads but have rooted up to 4 joined pads with no problems.
click it