  We study the magnetotransport properties of patterned 3D topological
insulator nanostructures with several leads, such as kinks or Y-junctions, near
the Dirac point with analytical as well as numerical techniques. The interplay
of the nanostructure geometry, the external magnetic field and the
spin-momentum locking of the topological surface states lead to a richer
magnetoconductance phenomenology as compared to straight nanowires. Similar to
straight wires, a quantized conductance with perfect transmission across the
nanostructure can be realized across a kink when the input and output channels
are pierced by a half-integer magnetic flux quantum. Unlike for straight wires,
there is an additional requirement depending on the orientation of the external
magnetic field. A right-angle kink shows a unique $\pi$-periodic
magnetoconductance signature as a function of the in-plane angle of the
magnetic field. For a Y-junction, the transmission can be perfectly steered to
either of the two possible output legs by a proper alignment of the external
magnetic field. These magnetotransport signatures offer new ways to explore
topological surface states and could be relevant for quantum transport
experiments on nanostructures which can be realized with existing fabrication
methods.
