Atomistic molecular dynamics (MD) simulations are carried out to examine the effect of molecular weight M-w (= 0.6, 0.86, 1.12, and 2.15 kDa) and pH (or equivalently, degree of ionization, a(+) = 0, 50, and 100%) on the structure, state of hydration, and dynamics of linear and branched poly(ethylene imine) (PEI) chains in infinitely dilute salt-free aqueous solutions. It is found that the degree of ionization is the key factor determining the type of molecular conformation adopted by PEI, regardless of molecular architecture and chain length, resulting in a stable trans conformation for fully ionized solutions and in a stable gauche(+)/gauche(-) state for neutral or alternate ionized ones; in the latter case, a strong electrolyte behavior is verified for both linear and branched PEI. Linear PEI is observed to be significantly stiffer than branched PEI of the same molecular weight at 100% degree of ionization, but the effect subsides as the degree of ionization decreases. Also, linear PEI diffuses markedly slower than branched PEI of the same M-w. From the MD results, scaling exponents are deduced and reported for the conformation, solvent-accessible surface area, and dynamics of the two different PEI structures with M-w.