A pointer to non-const data can be implicitly converted to a pointer to const data of the same type:
int *x = NULL;
int const *y = x;
Adding additional const qualifiers to match the additional indirection should logically work the same way:
int * *x = NULL;
int *const *y = x; /* okay */
int const *const *z = y; /* warning */
Compiling this with GCC or Clang with the -Wall flag, however, results in the following warning:
test.c:4:23: warning: initializing 'int const *const *' with an expression of type
'int *const *' discards qualifiers in nested pointer types
int const *const *z = y; /* warning */
^ ~
Why does adding an additional const qualifier "discard qualifiers in nested pointer types"?
The reason why const can only be added one level deep is subtle, and is explained by Question 11.10 in the comp.lang.c FAQ.
Briefly, consider this example closely related to yours:
const int i;
int *p;
int const **z = &p;
*z = &i;
/* Now p points to i */
C avoids this problem by only allowing assignment to discard qualifiers at the first pointed-to level (so the assignment to z here is not allowed).
Your exact example does not suffer from this problem, because the const the second level means that the assignment to *z would not be allowed anyway. C++ would allow it in this exact case, but C's simpler rules do not distinguish between your case and the example above.