  The connections between quasi-Assouad dimension and tangents are studied. We
apply these results to the calculation of the quasi-Assouad dimension for a
class of planar self-affine sets. We also show that sets with decreasing gaps
have quasi-Assouad dimension $0$ or $1$ and exhibit an example of a set in the
plane whose quasi-Assouad dimension is smaller than that of its projection onto
the $x$-axis, showing that quasi-Assouad dimension may increase under Lipschitz
mappings. Moreover, for closed sets, we show that the Hausdorff dimension is an
upper bound for the lower-Assouad dimension.
