Lattice model dendrimers interacting with an adsorbing planar surface are studied by computer simulation, where G is the number of generations of the dendrimer and A is the interaction strength. With increasing A, dendrimers are observed to spread out and flatten down on the surface, as expected. In certain regions of G-A space, two competing configurational states, S-2 and S-3, are observed. In S-3 all three dendrons are adsorbed on the plane. In S-2 two dendrons are adsorbed, while the third sits up and away from the surface. G-A space divides into five separate regions : a desorption region where A is too weak to maintain adsorption, a weak adsorption region in which the dendrimer tends to maintain contact but with only weak perturbation of its shape, a region in which S-2 and S-3 compete because they have comparable free energies and are separated by a modest free energy barrier, a region in which S-3 dominates because it has lower free energy, and finally a region in which S-2 and S-3 both have high stabilities because they are separated by a large free energy barrier.