Using all atomistic molecular dynamics (MD) simulations we report a microscopic picture of the carbon nanotube (6,5)-dendrimer complex for PAMAM dendrimers of generations 2 to 4. We study the compact wrapping conformations of the dendrimer onto the nanotube surface for all the three generations of PAMAM dendrimer. A high degree of wrapping for the non-protonated dendrimer is observed as compared to the protonated dendrimer. For comparison, we also study the interaction of another dendrimer, poly(propyl ether imine) (PETIM), with the nanotube. The results of the distance of closest approach as well as the number of close contacts between the nanotube and the dendrimer reveal that the PAMAM dendrimer interacts strongly as compared to the PETIM dendrimer. We also calculate the binding energy between the nanotube and the dendrimer using MM/PBSA methods and attribute the strong binding to the charge transfer between them. Dendrimer wrapping on the CNT will make it soluble and the dendrimer can act as an efficient dispersing agent for the nanotubes.