Linear trimethylene carbonate (1,3-dioxane-2-one, TMC) thermoplastic copolymers derived from glycerol have been synthesized upon sequential copolymerization. The “immortal” ring-opening polymerization (iROP) of the benzyloxy-substituted TMC, 3-benzyloxytrimethylene carbonate (BTMC), with systems composed of the β-diketiminate discrete zinc complex [(BDIiPr)Zn(N(SiMe3)2)] or the phosphazene base 2-tert-butylimino-2-diethylamino-1,3-dimethylperhydro-1,3,2-diazaphosphorine (BEMP) as a catalyst, and benzyl alcohol (BnOH) as an initiator/chain transfer agent is first described. Next, diblock and triblock copolycarbonates featuring a TMC segment along with one or two adjacent BTMC, or 2,2-dimethoxypropane-1,3-diol carbonate (TMC(OMe)2), or racemic β-butyrolactone (BL) chains have been prepared. The copolymerization under “immortal” operating conditions was carried out in bulk or toluene solution and promoted by [(BDIiPr)Zn(N(SiMe3)2)] as a catalyst, and either BnOH, 1,3-propanediol, or the poly(trimethylene carbonate) (PTMC) derived macro-ols, H-PTMC-OBn or H-PTMC-H, as an initiator/chain transfer agent. In particular, the PTMC-b-[poly(TMC(OMe)2)]1,2 couple of copolymers provide a basis for the assessment of thermal and mechanical property differentiation in close relationship with the co-monomers content. Unlike PTMC which is elastomeric and P(TMC(OMe)2) which is rather rigid and brittle much like semi-crystalline poly(L-lactide), the diblock and triblock copolymers show characteristics lying in between those of each homopolymer, without any significant influence of the topology. Thus PTMC/PTMC(OMe)2 block copolymers mechanically behave similarly to PTMC/PLLA block copolymers.