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We consider the most general class of teleparallel gravitational {}{}theoriesquadratic in the torsion tensor, in three space-time dimensions, and carry outa detailed investigation of its Hamiltonian formulation in Schwinger's timegauge. This general class is given by a family of three-parameter theories. Aconsistent implementation of the Legendre transform reduces the original theoryto a one-parameter family of theories. By calculating Poisson brackets we showexplicitly that the constraints of the theory constitute a first-class set.Therefore the resulting theory is well defined with regard to time evolution.The structure of the Hamiltonian theory rules out the existence of theNewtonian limit.Comment: 17 pages, Latex file, no figures; a numerical coefficient has been  corrected and a different result is achieve

Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge