A series of homologous dendronized polymers (DPs) with generations (g) 1-3 and backbone nominal degrees of polymerization (P-n) in the range 50-3000 have been synthesized and characterized in order to investigate the g- and P-n-dependent viscoelastic properties and packing of this class of densely grafted, associating and effectively "thick" macromolecules in their molten state. Rheological measurements reveal an unusually long thermal equilibration time, attributed to (i) the tendency of DPs to minimize local density gradients, as realized via their mutual weak interpenetration, and (ii) the intermolecular DP-DP correlations and inter- and intramolecular hydrogen bonding and pi-pi stacking interactions. With the help of simulations and X-ray scattering measurements, a scenario emerges, according to which DPs interact via local cooperative rearrangements of the dendrons, akin to a Velcro fastening process. In this picture, neighboring bonds accelerate the local interpenetration process. Results from X-ray scattering show increased lateral backbone-backbone correlations with a columnar arrangement of backbones and a liquid crystalline underlying order. Linear viscoelasticity is characterized by plateau moduli which originate from intermolecular bonding and whose extent in frequency and absolute value depends on P-n and g and can be lower than or comparable to that of the backbone. Very long relaxation times can be probed (sometimes via creep measurements) and attributed to the lifetime of the bonds. The nonlinear shear rheology data suggest a resemblance in behavior to unentangled linear chains with finite extensibility and point to reduced deformability of the DPs in flow. These findings indicate that DPs constitute a promising class of functional macromolecules with tunable properties.