  The Mott-insulating rare-earth titanates (RTiO$_3$, R being a rare-earth ion)
are an important class of materials that encompasses interesting spin-orbital
phases as well as ferromagnet-antiferromagnet and insulator-metal transitions.
The growth of these materials has been plagued by difficulties related to
overoxidation, which arises from a strong tendency of Ti$^{3+}$ to oxidize to
Ti$^{4+}$. We describe our efforts to grow sizable single crystals of YTiO$_3$
and its La-substituted and Ca-doped variants with the optical
travelling-solvent floating-zone technique. We present sample characterization
$via$ chemical composition analysis, magnetometry, charge transport, neutron
scattering, x-ray absorption spectroscopy and x-ray magnetic circular dichroism
to understand macroscopic physical property variations associated with
overoxidation. Furthermore, we demonstrate a good signal-to-noise ratio in
inelastic magnetic neutron scattering measurements of spin-wave excitations. A
superconducting impurity phase, found to appear in Ca-doped samples at high
doping levels, is identified as TiO.
