Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically tile variation of the glass-transition temperature (T-g) and the size v and number density N-h of local free volumes in n-alkyl-branched polypropylenes. The samples were metallocene-catalyzed propylene copolymers with different alpha-olefins (from C-4 to C-16) and a different alpha-olefin content (between 0 and 20 mol %). From the total specific volume and crystallinity the specific volume of the amorphous phase V-a was estimated and used to calculate the fractional free (hole) volume h and value of N-h. The variations of T-g, upsilon, V-a, h, and N-h were related to the degree (number and length) of branching. T-g decreases and v increases linearly with the number and length of n-alkyl branches, This behavior was attributed to an increased segmental mobility caused by branching. Both values, T-g and v, follow linear master curves as a function of the degree of branching (DB) if this is defined as the number of all side-chain carbons with respect to a total of 1000 (main-chain and side-chain) carbons. Only propylene/1-butene copolymers deviated from these relations. A linear relation between v and T-g was also found. The number density of holes was estimated to be N-h = 0.49(+/-0.07) nm(-3) and N-h' = 0.58(+/-0.11) x 10(21) g(-1), respectively. It shows a slight variation with the DB, which is also seen in the behavior of the specific volume V-a. This variation was explained by the appearance of sterical hindrances resulting from short-chain branches that may prevent an efficient packing of the chains.