There's actually more than that, and there are whole rafts of texts written about the subject. The intricacies are complicated, and well beyond the scope of what can be done here. I'd be looking for a taxation lawyer if you're wanting to set up the proper structure for a private equity fund.
thanks, but at least are those three correct and real options for equity fund?even though there are more (i'm looking for the main legal structure possibility for equity fund)
Yes, but they're all vastly different and whether or not they're 'real options' will depend on the makeup of the fund.
For example, to give you some reference point only, the number and sophistication of the participants will determine whether or not you must use a managed investment structure. If you've got a large number of investors who aren't sophisticated, then failing to use a managed investment structure will likely be illegal.