All the royalties, less production taxes and property taxes are paid out to the partners through distributions.  Conversely, if an individual receives the royalty, the royalty company does not reduce the royalty payment by depletion, it is up to the individual to claim the depletion on his/her tax return.  

As far as basis goes, this land was in the family for generations - they discovered oil on the land.  The family is splitting the royalty payments and claiming the income on their individual tax returns (less depletion).