The equilibrium theory of polymer adsorption on a solid/liquid interface is well established. De Gennes explained that linear homopolymers adsorbing on a surface develop a proximal, central, and distal region in their adsorption profile, wherein the central region has a universal scaling self-similar structure with power-law coefficient -4/3. More pictorially, the layer is composed of trains, loops, and tails. Linear chains have just two tails, and therefore it is often assumed that the adsorption layer consists of loops only. Branched macromolecules have multiple tails, and the loops-only approach is argued to become progressively less accurate. Using self-consistent field theory of Scheutjens and Fleer (SF-SCF), we consider the macrocycle (chain without ends), linear, star-like, dendritic, and comb-like (homo)polymers and focus on the effects of tails. We show that the adsorption profile changes systematically with the degree of branching. Typically, for significantly branched chains the polymer density in the outer part of the central region has an effective scaling coefficient that may exceed the -4/3 value. Comb polymers adsorb with their backbone preferentially and generate a "brush"-like layer through adsorption, which we refer to as a hedge layer as the backbone and branches are hidden behind the free ends. By way of an array of "out-going"side chains, such a layer acts as a superb colloid stabilizer and as a lubricant, outperforming star-like polymers or dendritic polymers which qualitatively behave similar to linear chains.