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If I have a poncho or space blanket, I use it inside the debris shelter rather than on top. This is in part because putting a small space blanket on top doesn't cover much of the "roof", in part because I think they are more effective directly on you or directly over the sleeping bag (in the cold, at least), and partly because I often need to take the poncho with me in the day time. If it's just wrapped around my sleeping bag or poncho liner (warmer weather), I can take it with me more easily than if its integrated into the debris shelter. I also find that putting a space blanket or thin tarp on a debris shelter results in holes pretty quickly.
Just my .02
One issue with using a tarp or tarp substitute as part of the roof of a shelter is avoiding damage to the "tarp." I have seen trash bags and "survival blankets" riddled by twings and branches in the course of throwing the shelter together ("throwing"!). Because the shelter was just large enough to hold the "survivor," it would have worked out but for the holes.
If the "tarp" part of the shelter, the interior is kept drier, which may be more comfortable if you have to stay inside it for a time.
A "third way" is to rig the "tarp" as a wedge or A shape inside the shelter (like over some paracord). That allows more room and air circulation.