We give a generalization of the theory of flocks of hyperbolic quadrics in PG$(3,q)$ to what is called an $\alpha$-twisted hyperbolic flock in an arbitrary $3$-dimensional projective space over a field $K$. We obtain an equivalence between a set of translation planes with spreads in PG$(3,K)$ that admit affine homology groups such that the axis and coaxis and one orbit is a twisted regulus. Examples and generalizations are also given.

SL$((2,q)$-unitals are unitals of order $q$ admitting a regular action of SL$((2,q)$ on the complement of some block. They can be obtained from affine SL$((2,q)$-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine SL$((2,q)$-unitals and show that exactly two parallelisms are fixed by all automorphisms. In nonclassical SL$((2,q)$-unitals obtained as closures of affine SL$((2,q)$-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.

To the knowledge of the author no dimensional dual hyperovals of elliptic or parabolic type have been described yet. The purpose of this note is to fill this gap.