Whew.... well here goes on the topic of Wobbegongs.
Anyway... there are several species of wobbegongs and generally speaking they are all wonderful display animals, except some just get very large for standard home systems. All species are from reefs and they are only found in Australia, South Pacific, and South Japan. They are all ambush preditors which means they just sit and wait for their food to come to them. It is common for wobbegong owners to feed them with some sort of pole arm. It is very difficult to select tank mates for wobbegongs because, in general fish aren't very inteligent, and they will wander right up to the wobbegongs fringed sea-weed like appendages and be gobbled right up. At night wobbegongs will stalk prey like octopus, squid, other sharks, fish, and crabs. Wobbegongs don't need a reason to eat tankmates they just will. Wobbegongs will attack humans unprovoked. They don't feed very frequently, and when they do they don't always feed till they are full. Chances are your newly aquired wobbegong will not eat when you introduce him into the tank. You may need to feed him feeder goldfish or silversides for a long time.. until he will willing except shrimp or squid. For a long time my wobbegongs would bite squid and then just spit it out after about 30 seconds so I had to feed them feeders. Wobbegongs unlike other sharks are not sensitive to copper based medications. They also live in a very low salinty range about 1.018 to 1.024.
I will talk about Japanese and Wards wobbegongs since I doubt any of you will be springing for something larger. They both are less than 42" at full growth and since they are so lethargic and hardly move they do not require large tanks. However they do require massive amounts of water movement. When I say massive I mean in the area of one 1,000 to 1,500gph pump per 200 gallons. The Japanese wobbe will eat shrimp, groupers, tilefish, parrotfish, scorpionfish, skates, sea robins, shark egg cases, and many other fish and crusteceans. They need water temperature about 60 to 78 degrees... anymore than that could be fatal. So a chiller is almost required.
Wards wobbe are less aggressive fish. They most likely will not bite you unless you are holding their food. It will need all of the above listed care requirerments except they can live in 72 to 82 degree water. This type of wobbegong is MUCH more difficult to find, but more suited to aquarium life especially when you have other tankmates.
You will need a minimum 150 gallon tank for both fish... if you are going to have lots of live rock and other tank decor I would suggest a 250 or 260. UV sterlization isn't a priority but will indeed be a nice addition. Excess protien skimming and wet/dry filtration is essential for small aquariums housing sharks. In large tanks like 6,000 gallon and over protien skimming isn't required. Something more in the lines of massive fluidized bed filters are important in those cases. So you can never have enough skimming essentially.
Tankmates - there isn't much I can say about. It at your risk only. I don't keep anything in my tanks with my wobbegongs except VERY large sharks... ones they can't possibly eat. Nurse sharks and black tips things like that. If you insist on having tank mates... lionfish, golden trevallys, banded coral shrimp, very large rays, hawkfish, very large moray eels, cardnalfish, and groupers is about all I can suggest. Damsels will be dead meat even though they are sometimes recommended. I have seen my wobbegongs eat 20-25 blue devil damsels in less than 3 hours. Don't waste your money. Brittle stars, slipper lobsters, and pencil urchins might work as well. I would not recommend a remora. They are a very harassing fish and will undoubtedly steal all the food you place in the tank. This will cause the remora to get very large and destructive, and take it from me, ALL fish stores hate remoras. So good luck getting rid of it. I do keep lots of cleaner wrasse in my tanks to clean parasites from my sharks, but they are also potential dinners for wobbegongs so just be careful of that.
Jim