Do you mean our Permanent Fund Dividend checks? These come as dividends to stockholders. A percentage of oil royalties paid to the State are invested in a Permanent Fund, which is in turn invested in the national and international market. Once each year, the dividends on these investments are calculated and divided among the stockholders (thats us, we Alaskans). Sarah Palin was not the designer of, nor had she anything to do with this program. It was put into place before the pipeline was built, back in the Seventies.
This might help you get up to speed on what Palin did as Governor. She did in deed impose a “Windfall” tax. To cover increases in the price of oil. Read the whole article. explains it in great detail, especially in regards to the Permanent Fund;
http://seattletimes.nwsource.com/html/businesstechnology/2014601450_alaska27.html
This additional tax was SP's baby and was layered on top of the royalties and other existing fees. It was an aggressive progressive tax on net profits.
According to industry officials it brought Alaska's share of revenue (revenue - not profits) up to 75%.
Part of the revenue derived from this additional tax did go to Alaskans in the form of a check. But, and this is key, this was not an agreed upon quid pro quo driven royalty...it was a levied tax and as with any tax those entities paying had no say in the matter.
To take it a step further, it was a tax (confiscation) of corporate revenues for the purpose of re-distribution.