Template argument deduction is done by comparing the return type of the conversion function template (call it P) with the type that is required as the result of the conversion (call it A; see [dcl.init], [over.match.conv], and [over.match.ref] for the determination of that type) as described in [temp.deduct.type].

If P is a reference type, the type referred to by P is used in place of P for type deduction and for any further references to or transformations of P in the remainder of this section.

If A is not a reference type:

If P is an array type, the pointer type produced by the array-to-pointer standard conversion ([conv.array]) is used in place of P for type deduction; otherwise,

If P is a function type, the pointer type produced by the function-to-pointer standard conversion ([conv.func]) is used in place of P for type deduction; otherwise,

If P is a cv-qualified type, the top level cv-qualifiers of P's type are ignored for type deduction.

If A is a cv-qualified type, the top level cv-qualifiers of A's type are ignored for type deduction. If A is a reference type, the type referred to by A is used for type deduction.

In general, the deduction process attempts to find template argument values that will make the deduced A identical to A. However, there are two cases that allow a difference:

If the original A is a reference type, A can be more cv-qualified than the deduced A (i.e., the type referred to by the reference)

The deduced A can be another pointer or pointer to member type that can be converted to A via a qualification conversion.

These alternatives are considered only if type deduction would otherwise fail. If they yield more than one possible deduced A, the type deduction fails.

When the deduction process requires a qualification conversion for a pointer or pointer to member type as described above, the following process is used to determine the deduced template argument values:

If A is a type

cv_{1,0} “pointer to …” cv_{1,n-1} “pointer to”
cv_{1,n}T1

and
P
is a type
cv_{2,0} “pointer to …” cv_{2,n-1} “pointer to”
cv_{2,n}T2

The cv-unqualified
T1
and
T2
are used as the types of
A
and
P
respectively for type deduction.
[ ```
struct A {
template <class T> operator T***();
};
A a;
const int * const * const * p1 = a; // T is deduced as int, not const int
```

* — end example* ]