  Given a handle decomposition of a 4-manifold with boundary, and an open book
decomposition of the boundary, we show how to produce a trisection diagram of a
trisection of the 4-manifold inducing the given open book. We do this by making
the original proof of the existence of relative trisections more explicit, in
terms of handles. Furthermore, we extend this existence result to the case of
4-manifolds with multiple boundary components, and show how trisected
4-manifolds with multiple boundary components glue together.
