If multiple players each control Treasure Nabbers, an artifact tapped for mana will make quite a journey. For example, if player A taps an artifact for mana during their turn, and players B and C are the next players in turn order who control Treasure Nabbers, C's ability resolves before B and C gains control of the artifact. Then B gains control of the artifact. B keeps it during their turn, and then C regains control of the artifact once B's effect expires, then A will have it back after C's expires. However, if B or C taps the artifact for mana, one of them will take it from the other. You may need to pay very careful attention to which effects are still in effect, which have expired, and who owns what.