Alan: I wasn't dissasociating law from the domain holdings, merely avoiding giving the province level itself income by adding income to the law holding - the existing tie to holdings would have been retained, my apologies for being unclear. Also, unless I'm mis-reading it (quite possible) the P&H shows that there is currently <no> income from provinces - currently you only appear to get income from holdings.
I think you are mis-reading it. Currently, a law holding draws income from 5 potential sources: manors, temples, guilds, trade and province.
Graciously put sir, column R was hidden if the sheets I was looking at and when I deleted province taxation (col S) nothing happened so I assumed that it had been cut out of the law income calculation and was simply a redundant leftover.
Looking more closely at the formula, law holdings are picking up the enhanced province level directly (col R), multiplying it by law level over 5 and then modifying the result for prosperity - completely bypassing the province taxation calculation itself in column S which in turn looks to be calculating the post-law income from the province but is in fact apparently completely redundant - it doesn't appear feed into the regent income totals so "1b" below would appear already in effect albthough that contradicts the province squared comment as that requires province taxation to be included for total province income to be the swuare of province level at average prosperity.
If however Col S is not going to feed into income - and 1b suggests that it won't - then law holdings will have to generate the extra income desired for rulers, which directly conflicts with point 4 - there doesn't appear to be another route for the province ruler to get more income other than via law holdings.
I'm probably too tired to figure out the plan, as if the plan is to give more income to rulers (1a) then it has to either come from the province taxation in column S that is currently lost (barred under 1b), or via law holding collections (barred under 4). I'm also getting confused between what is proposed and what is changing as most of the proposals made appear to be effective already, and I'm not sure what is meant by "province taxation" in various comments - the income directly from the province level in col S, or the law holding claim thereon.
I can't help but feel that the best way to get 1a, while keeping 3 and 4, is to dump 1b in the skip. To pump "4" you could exempt province taxation from law holding collection leaving the province ruler pumped up at the expense of law regents with no impact on other domains. If the aim is to drop domain income while pumping law holders then it would be simpler to raise the tax rate percentages then change divisors.