The anisotropy of the azimuthal distributions of charged particles produced in root s(NN) = 2.76 TeV PbPb collisions is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter, upsilon(2), defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee-Yang zeros. The anisotropy is presented as a function of transverse momentum (p(T)), pseudorapidity (eta) over a broad kinematic range, 0.3 < p(T) < 20 GeV/c, vertical bar eta vertical bar < 2.4, and in 12 classes of collision centrality from 0 to 80\%. The results are compared to those obtained at lower center-of-mass energies, and various scaling behaviors are examined. When scaled by the geometric eccentricity of the collision zone, the elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies. DOI: 10.1103/PhysRevC.87.014902