If there is an LP formed to share equity, it will be between the corp entities (as Partners), not the common shareholders of the corps. The net income (or loss) would then accrue to the corp partners. The reason for doing this is to allow PXD or some other corp to buy an equity interest in specific assets of ERHE. These assets would be contributed to the partnership, and PXD would contribute an equal amount of cash, or some other amount, depending on the % ownership. ERHE and PXD would accrue the earnings of the partnership based on their % contribution (or other contractually agreed %). This is a very common type of organization in real estate, mineral deals, etc.
JMO, Magic