lighter wire gauge, etc. questions

[tokki g]

What is the gauge of the power and ground wires for the cig lighter (on the arm rest next to the ashtray) in our cars? I have a 10-12ga wire /w an inline 1amp fuse that I want to attach to the power wire, but it's way too big to fit the cig lighter power wire. I went to radioshack and they didn't have any wire splitters that could take a 24ga (this is my guess at the gauge of the cig lighter power wire) input and split it out to a 10ga and another 24ga. Hopefully those exist...?
Alternatively, I'm hoping I can find some butt connectors that can connect 22+ ga to 10-12ga. Do these exist? If so, then that would make everything a lot easier.

Edit: Just gonna use ring terminals. N00b move...