The 1Sigma(u)+ excited states of the H2 molecule are computed following a recent study by Corongiu and Clementi (J. Chem. Phys. 2009, 131, 034301) on the 1Sigma(g)+ states. Full configuration interaction computations both from Hartree-Fock molecular orbitals and Heitler-London atomic orbitals are presented and correlated with a comprehensive analysis. The basis sets utilized are either extended and optimized Slater type functions, STO, or spherical Gaussian functions, GTO. Computations and analyses are presented for states 1 to 14, covering the internuclear distances from 0.01 to 10000 bohr. The accurate data by L. Wolniewicz and collaborators, available for the first six excited states, verify the good quality of our computations. We focus on the characterization of the orbitals in the excited state wave functions, on the electronic density evolution from the united atom to dissociation, on quantitative decomposition of the total energy into covalent and ionic components and on detailed analyses of energy contributions to the total state energy from selected STO subsets. Each manifold has one state, specifically the states 1, 3 and 6, where the second minimum has strong ionic character. State 10 dissociates into the ion pair H+H-.