  We compare self-joining- and embeddability properties. In particular, we
prove that a measure preserving flow $(T_t)_{t\in\mathbb{R}}$ with $T_1$
ergodic is 2-fold quasi-simple (2-fold distally simple) if and only if $T_1$ is
2-fold quasi-simple (2-fold distally simple). We also show that the
Furstenberg-Zimmer decomposition for a flow $(T_t)_{t\in\mathbb{R}}$ with $T_1$
ergodic with respect to any flow factor is the same for
$(T_t)_{t\in\mathbb{R}}$ and for $T_1$. We give an example of a 2-fold
quasi-simple flow disjoint from simple flows and whose time-one map is simple.
We describe two classes of flows (flows with minimal self-joining property and
flows with the so-called Ratner property) whose time-one maps have unique
embeddings into measurable flows. We also give an example of a 2-fold simple
flow whose time-one map has more than one embedding.
