Who pays for the primaries?

[True Federalist (진정한 연방 주의자)]

When states run primary elections are they paid 100% by the tax payer? Meaning voting booths, etc? And if so, why? Primaries aren't even required by the law or the Constitution, shouldn't the parties pay for a portion of the costs?

I think it varies from state to state. Most states do use taxpayer money, I believe.....I think I heard once that the parties pay for them in South Carolina, for example.

South Carolina used to have party-run and paid for Presidential primaries, but that stopped being the case in 2008, provided that your party received at least 5% of the vote in the last Presidential election. In other words, they wrote the law to pay for just the Republican and Democratic presidential primaries, but not those of other political parties.

[True Federalist (진정한 연방 주의자)]

Do the Dems and GOP still control the timing of the presidential primaries in SC, or is that now set by the state legislature?

They do, subject to a requirement that they inform the State at least 90 days in advance of the date if they expect the State to pay for it.  They can also set polling hours other than the usual 7 am to 7 pm.  Also the primary must actually select who the delegates vote for.  If the primary is merely to suggest to the party convention, then the party has to pay for it.  Oddly enough they wrote the provision so that without them passing further changes to the law, it applied only to 2008.  I suspect they may have done that so that if a Republican had won in 2008, then the law would automatically revert for 2012 so that the Democrats would have to pay for their primary to see who would face the Republican incumbent themselves.