J Lo and A-Rod took a smaller boat over to Arison's legendary Sirona III -- a 185-foot floating palace that fits 12 guests in 5 state rooms.

It's got a hot tub on deck, a sick bar area, a gym and plenty of deck space to take in some sun while sipping on boat drinks (shout out Jimmy Buffett).

J Lo came looking the part -- wearing an airy white dress, wedge sandals and a fancy Chanel bag in hand. Alex Rodriguez was there too.

So, what do these 3 insanely rich people talk about on the yacht? Whatever they want.

Happy sailing ...