There are successful protocols for dispersing carbon nanotubes and graphene oxide in physiological media by using biocompatible polymers, which enable their use in nanomedicine. However, there is not a clear understanding regarding the mechanisms of the colloidal stabilization manifested (i.e., electric, steric or electrosteric or through depletion forces). Here we show that the manifestation of a particular mechanism of stabilization for oxidized carbon nanotubes (CNTs) and graphene oxide (GO) in the presence of Pluronic F-127 (PF127) and short-and long-chain polyethylene glycol (PEG 1,500 or 35,000 respectively) depends on a proper matching between the nanocarbon morphology and the polymer chain length, chemical structure and concentration. The high aspect ratio one dimensional morphology of CNTs enables an initial steric and electrosteric stabilization through the nanotube wrapping (i.e., adsorption) by PF127 present in low concentrations (<0.1%). Depletion stabilization for CNTs manifests when PF127 is present in high concentrations (≥1.0%), thus enabling the formation of highly stable CNT colloids even in a 0.9% NaCl saline solution. This depletion stabilization depends little on the CNT structure (i.e., single-or multi-wall), surface charge (i.e., zeta potential), oxidation and carboxylation degree or the nanotube length. On the other hand, large-sized sheets of GO could be colloidally stabilized in NaCl 0.9% only in the presence of PEG 35,000 through repulsive depletion forces, whose manifestation occurs with a polymer concentration threshold of 5.0 wt%. Comparatively, in a physiological saline solution, PF127 is able to colloidally stabilize CNTs to a much large extent than PEG 35,000 stabilizes the large GO sheets.