WHO OWNS THE SWARM written from the point of view of the owner of the hive from which the bees have swarmed.   With acknowledgement of Andrew Beer

SWARM OWNERSHIP INDICATOR SITUATION OWNER WHY?
A. Bees in your hive; your colony shows evidence of swarm plans e.g. larvae in queen cells but no swarm has emerged. You Those in hive belong to you.
B. Bees out of the hive on “colony business” – not in swarm. You Their intention is to return to the hive.
C. Bees in swarm and you did not see them emerge. No one. Your ownership is lost when the swarm emerges [but may be regained – see E below]. Bees have reverted to wild state over which you have no control, and nor does anyone else.
D. Bees in swarm and you saw them emerge. No one but your right to follow them starts. You can become the owner of the swarm if you can take it under E or F below. A beekeeper who sees his swarm emerge has a right to follow them (see below).
E. Bees in swarm described in C or D have landed – i) on your land. ii) on somebody else’s private property. i) You if you catch them and to the extent that they remain under your control. ii) You if you are allowed access and you catch them, as above. N.B. If someone else takes them, whether the property owner or a person authorised by the property owner does so, he/she becomes the owner. (i) and (ii). Control gives you ownership
F. You have successfully followed and collected the swarm described in D. You. Based originally on Roman Law a beekeeper who keeps his swarm in view and collects it, can claim it. But if the swarm settles on private land, the right to follow and claim is lost.
G. Swarm has got away, living wild anywhere, including your land. No one. No one controls it.