Separated Co-granules, of an average diameter as small as D = 2.0 nm, of FCC crystal structure have been synthesized by co-reducing Co2+ cations dispersed in a liquid. They exhibit an enhanced saturation magnetization sigma(s) by as much as similar to 34% with a more than an order of enhanced magnitude for the effective anisotropy constant K-eff over the bulk values at 4.2 K. An irreversibility in the ZFC-FC (zero field cooled-field cooled) thermomagnetograms occurs at temperatures T less than or equal to T-B, where T-B is their blocking temperature. The ZFC thermomagnetogram peaks at T-B according to their K-eff and volume V. T-B = 152 K has been found for D = 10 nm granules in an applied magnetic field of H = 1 kA/m. The sample, which is superparamagnetic (coercivity H-c = 0) in nature at T greater than or equal to T-B, develops H-c at T < T-B with a unique dependence on temperature, H-c(T) = H-c(0)[1 - T/T-B](1)/2, with H-c(0) = 40.0 kA/m. The results are discussed with a two-phase model structure of granules. In this model, the grain-surface atoms have a modified magnetic structure of the core atoms. An inter-coupling between the magnetic spins in the two regions occurs in a ferromagnetic or antiferromagnetic manner according to their interface that mediates their exchange interactions through it. The studies of sigma, K-eff, or H-c as a function of temperature (4.2 to 380 K) and/or size D (2 to 20 nm) demonstrate their strong correlation with the dynamics of the surface spins (DSS). An enhanced surface anisotropy with large total interface-energy in small granules governs the DSS. An average value of the surface anisotropy constant K-s = 2.28 mJ/m(2) is determined by a linear plot of K-eff with D-1 at D less than or equal to 2.9 nm. Larger granules follow a modified K-eff - D-1 plot with an order of smaller K-s-value. The surface spins form a surface-spin-glass, which undergoes a magnetic transition to a spin-frozen state at a critical temperature T-F = 71 K. The T-F evolves following the well-known de Almeida-Thouless line, delta T-F proportional to H-2/3, at H less than or equal to 42 kA/m.