I am wiring a new house. I bought a boat load of new Romex wire size 10, 12, and 14. I've used all my 12 and 14; is it alright to use the number 10 in place of number 12?
Is it safe to pigtail from 10 gauge down to 12 gauge? Yes, as long as you are not exceeding the power limits of the 12 gauge wiring or the receptacles.
For those who may need a simple example, we do this all of the time - The house itself receives power from 0 gauge wire into the distribution box, and from there we put in an appropriate sized breaker, and use 12 gauge or 14 gauge wiring from there on in.
Is it recommended? Not by a long shot, especially for a whole house job.
You are not saving time OR money by cobbling 10 gauge into 12 gauge.
More boxes, More wire nuts, more effort: Pigtailing to proper connection sizes means more than doubling the size of each junction box or it will require two boxes instead of one, as well as needing twice as many wire nuts.
Your code inspectors may not like it: You normally need a "pre-install" inspection, which has the raw runs (without receptacles installed) exposed. They may red flag these junctions, making you pull off each one and reinspect, then reconnect them all and reinspect, then install receptacles and switches and inspect.
Also, not sure how your inspection forms get filled out, but doubling the number of boxes to be inspected may become a problem, including additional fees. Again, definitely not worth the headache.
The best answer is to return 10 gauge and run the recommended sizes for the runs.
Many places will take back the wire, as long as it looks unused. They can put it back on the wire spools and resell it at a higher price for custom lengths.