Runny yolks, hopefully NO hard cooked yellow, but the whites must be firm. Any wobbly, jellyish white immediately gets removed from my plate, as I can’t abide even looking at it.
I often make over-easy eggs whereby I cut the whites off and eat them, and then gently lift the yolks onto toasted and buttered English muffin halves. The yolk gets carefully stabbed and gently cut up so the runny yolk seeps into the nooks and crannies, and then the English muffin half gets eaten that way. Depending on how yolky the egg is, yes, it’ll run down my fingers.
Whereas my late stepfather always broke the yolk in the pan so they’d cook a bit. We’d always argue (friendly tones! LOL) that the other’s way of cooking/eating eggs was sacrilege.