  We construct the global phase portraits of inflationary dynamics in
teleparallel gravity models with a scalar field nonminimally coupled to torsion
scalar. The adopted set of variables can clearly distinguish between different
asymptotic states as fixed points, including the kinetic and inflationary
regimes. The key role in the description of inflation is played by the
heteroclinic orbits which run from the asymptotic saddle points to the late
time attractor point and are approximated by nonminimal slow roll conditions.
To seek the asymptotic fixed points we outline a heuristic method in terms of
the "effective potential" and "effective mass", which can be applied for any
nonminimally coupled theories. As particular examples we study positive
quadratic nonminimal couplings with quadratic and quartic potentials, and note
how the portraits differ qualitatively from the known scalar-curvature
counterparts. For quadratic models inflation can only occur at small nonminimal
coupling to torsion, as for larger coupling the asymptotic de Sitter saddle
point disappears from the physical phase space. Teleparallel models with
quartic potentials are not viable for inflation at all, since for small
nonminimal coupling the asymptotic saddle point exhibits weaker than
exponential expansion, and for larger coupling disappears too.
