A systematic investigation on Mg doped and undoped InGaN epilayers grown by plasma-assisted molecular beam epitaxy has been conducted. Single phase InGaN alloys across the entire composition range were synthesized and Mg was doped into InxGa1-xN (0.1 <= x <= 0.88) epilayers up to similar to 10(20)/cm(3). Hall effect, thermopower, and electrochemical capacitance voltage experimental results demonstrate the realization of p-type InGaN across the entire alloy composition range for properly Mg doped InGaN. Hole densities have been measured or estimated to be in the lower similar to 10(18)/cm(3) range when the net acceptor concentrations are in the lower similar to 10(19)/cm(3) range across the composition range. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4795718]