Can you change from 10 or 8 gauge wire to 12 gauge in a 20amp circuit?

I'm attempting to extend a circuit with a few more outlets in a basement room. When I purchased the home they told me the previous owner was an electrician who self-built and wired the room. The room is on a 20amp breaker so I gathered all my materials, 12-2 wire, 20amp rated outlets and wingnut connectors. I... show more I'm attempting to extend a circuit with a few more outlets in a basement room. When I purchased the home they told me the previous owner was an electrician who self-built and wired the room. The room is on a 20amp breaker so I gathered all my materials, 12-2 wire, 20amp rated outlets and wingnut connectors. I found the final outlet in the current setup, but when I pulled it out I found that the wire they used looks to be 10 or possibly even 8 gauge. I don't have a tool to check for sure.

I know it's okay to use a higher than needed gauge from the panel out, but I don't know if it's okay to continue out from the current outlet with my 12-2 to the new outlets. Would variation in voltage be an issue? All in all, I plan to add an additional 5 outlets. Besides that, I'm following standard configuration with 12-2 wire (2-pair+ground), and pig-tailing the grounds.

Would I be okay to mix them like this?
Update: EDIT: Simplifying the question: Can I continue to branch off of #10/#8 wire on a 20amp circuit with #12 wire without a problem? Ignoring the fact of confusing future homeowners/electricians.
Update 2: There are currently only two receptacles on the circuit I'm looking to branch from - 2 outlets. So I have plenty of room for the expansion I want to do; I've already made sure to check this. That's not the question being asked here anyway, so please avoid talking about it and focus on the main question,... show more There are currently only two receptacles on the circuit I'm looking to branch from - 2 outlets. So I have plenty of room for the expansion I want to do; I've already made sure to check this. That's not the question being asked here anyway, so please avoid talking about it and focus on the main question, thank you.
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