We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in M. Aouchiche, P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2) (2011) 95--102. We also establish maximal trees for the difference of average eccentricity and remoteness and minimal trees for the difference of remoteness and radius proving thus that the corresponding conjectures posed in M. Aouchiche, P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2) (2011) 95--102 hold for trees.