what is return type of new in c++?

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There’s two things you have to distinguish. One is a new expression. It is the expression new T and its result is a T*. It does two things: First, it calls the new operator to allocate memory, then it invokes the constructor for T. (If the constructor aborts with an exception, it will also call the delete operator.)

The aforementioned new operator, however, comes in several flavours. The most prominent is this one: 

void* operator new(std::size_t);

You could call it explicitly, but that’s rarely ever done.

There are other forms of the new operator, for example for arrays

void* operator new[](std::size_t);

or the so-called placement new (which really is a fake-new, since it doesn’t allocate): 

void* operator new(void*, std::size_t);

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