  We perfect the recursion-transform method to be a complete theory, which can
derive the general exact resistance between any two nodes in a resistor network
with several arbitrary boundaries. As application of the method, we give a
profound example to illuminate the usefulness on calculating resistance of a
nearly $m\times n$ resistor network with a null resistor and three arbitrary
boundaries, which has never been solved before since the Greens function
technique and the Laplacian matrix approach are invalid in this case. Looking
for the exact solutions of resistance is important but difficult in the case of
the arbitrary boundary since the boundary is a wall or trap which affects the
behavior of finite network. For the first time, seven general formulae of
resistance between any two nodes in a nearly $m\times n$ resistor network in
both finite and infinite cases are given by our theory. In particular, we give
eight special cases by reducing one of general formulae to understand its
application and meaning.
