Hi all, Tom Fiore wrote:

Theorem. 9.17 Let X and A be strict 2-categories, and G:A -> X a pseudo functor. There exists a left biadjoint for G if and only if for every object x of X there exists an object r of A and a biuniversal arrow x -> Gr from x to G.

Of course this begs the obvious question, how hard is this to generalise to bicategories? I'm surprised no-one has mentioned Gurksi's thesis, which I just came across. Appendix A has details of adjunctions in bicategories, and biadjunctions in tricategories, citing Verity's thesis in the case of Gray-categories. Best, David