How do you capture mesprit azelf and uxie?

Answer 1

Go to the three lakes and find the island in the middle sneak up behind them and paralyze or make them sleep then throw the ball with the highest catch rate you have and if they escape walk around in the closest grass and it will come to you.

Answer 2

uxie and azelf they are like any boss battle they stay there but bosses like mesprit and there's one more they travel every where so its harder uxie and azelf they are just less defensive so when ever you use a attack that may knock them out when you about level 50 or up they will get knocked out so the trick is to use weaker Pokemon and use effective moves mesprit is diffrent because you have go every where to get mesprit a trick to catch it is to use mean look note golbats have this move then they wont be able to flee and mesprit will be forced to fight you hope this helps sorry if its long