Paradoxical Outcome will not resolve (i.e. 'fizzle', though that term does not appear in the rulebooks) if you target only one permanent and that leaves the battlefield before it resolves. Otherwise, if there are any legal targets left, all of these will still be returned to their owners' hands and you'll draw some cards (one for each of those permanents you own).
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard. Otherwise, the spell or ability will resolve normally. Illegal targets, if any, won’t be affected by parts of a resolving spell’s effect for which they’re illegal. Other parts of the effect for which those targets are not illegal may still affect them. If the spell or ability creates any continuous effects that affect game rules (see rule 613.10), those effects don’t apply to illegal targets. If part of the effect requires information about an illegal target, it fails to determine any such information. Any part of the effect that requires that information won’t happen.
The next step in spell resolution is
608.2c The controller of the spell or ability follows its instructions in the order written.
which will happen if it still has legal targets.