If you have a capital loss carryover of say $10,000 and the next year you have a gain of $30,000, does the ENTIRE loss carryover reduce the gain OR just $3000/year

Yes it will use the whole 10,000 carryover and to reduce the gain.  You get to first offset the loss against any gains you have each year so that can use more of it up. Then after applying the loss to the current gains you can take a max loss of 3,000 per year. 

The entire loss reduces the gains.  So the carryover amount is completely used.

Yes, the entire loss carried forward will be used, but there are limits. Losses on your investments are first used to offset capital gains of the same type. So, short-term losses are first deducted against short-term gains, and long-term losses are deducted against long-term gains. Net losses of either type can then be deducted against the other kind of gain.

Please read this TurboTax article for more information.