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An efficient density matrix renormalization group (DMRG) algorithm ispresented and applied to Y-junctions, systems with three arms of $n$ sites thatmeet at a central site. The accuracy is comparable to DMRG of chains. As inchains, new sites are always bonded to the most recently added sites and thesuperblock Hamiltonian contains only new or once renormalized operators.Junctions of up to $N = 3n + 1 \approx 500$ sites are studied withantiferromagnetic (AF) Heisenberg exchange $J$ between nearest-neighbor spins$S$ or electron transfer $t$ between nearest neighbors in half-filled Hubbardmodels. Exchange or electron transfer is exclusively between sites in twosublattices with $N_A \ne N_B$. The ground state (GS) and spin densities $\rho_r = <S^z_r >$ at site $r$ are quite different for junctions with $S$ =1/2, 1, 3/2 and 2. The GS has finite total spin $S_G = 2S (S)$ for even (odd)$N$ and for $M_G =S_G$ in the $S_G$ spin manifold, $\rho_r > 0 (< 0)$ at sitesof the larger (smaller) sublattice. $S$ = 1/2 junctions have delocalized statesand decreasing spin densities with increasing $N$. $S$ = 1 junctions have fourlocalized $S_z = 1/2$ states at the end of each arm and centered on thejunction, consistent with localized states in $S$ = 1 chains with finiteHaldane gap. The GS of $S$ = 3/2 or 2 junctions of up to 500 spins is a spindensity wave (SDW) with increased amplitude at the ends of arms or near thejunction. Quantum fluctuations completely suppress AF order in $S$ = 1/2 or 1junctions, as well as in half-filled Hubbard junctions, but reduce rather thansuppress AF order in $S$ = 3/2 or 2 junctions.

Efficient Density Matrix Renormalization Group algorithm to study Y-Junctions with integer and half-integer spin