Perhaps a black hole of minimal radius, like a Planck black hole, has the maximal entropy density of any physical entity. It has the maximal classical entropy density for black holes, and in addition its surface area topology ("entropy") fluctuates with spacetime extremes from quantum uncertainty.
I hate to admit it, but I really can't understand the question. What on Earth do you mean by a black hole of 'maximal radius'? That would be the entire Universe.