We have studied a system which consists of long, single chains of double-stranded DNA (contour length 57 μmm) interacting with cationic nanoparticles (NP) with diameters 10 (S), 15 (M), 40 (L) and 100 nm (XL) to study mechanisms of three-dimensional complexation between semi-flexible chain and nanospheres. There are three distinct mechanisms of DNA compactization by nanoparticles that can be realized depending on nanoparticles' sizes, DNA stiffness, and charge density on both components of interaction. In the case of large nanoparticles, a large amount of DNA is adsorbed electrostatically on the positively charged surface of each nanoparticle. When size of nanoparticle becomes smaller, rigidity of DNA chain becomes a critical factor, which prevents free DNA absorption on nanoparticle surface and another mechanism is realized: DNA wraps around a nanoparticle. By this mechanism, DNA compaction is achieved though wrapping around nanoscale objects, which mimics DNA packaging by histone core particles. In the case of even smaller particles, DNA chain cannot bend sufficiently to wrap around cationic nanosphere, and the complexation proceeds by the third mechanism: collection of small nanoparticles along DNA chain.