joining a table whose name is stored in the primary record

I've tried everything I can think of here to join records when the join
table varies and is named in the primary record, but to no avail. Here's
an example with all non-essentials stripped out.

I have 3 tables:

create table zip (
id serial primary key,
name text,
parent_tbl text,
parent_id int
);

create table city (
id serial primary key,
name text
);

create table county (
id serial primary key,
name text
);

The zip table has 2 records as follows:
id|name|parent_tbl|parent_id
-----------------------------
1 |10001|city |12
2 |19999|county |99

The possible parent tables can be many more than the two examples, city
and county.

In a single psql statement, I want to retrieve zip records joined with
the record of their respective parents. The join id is in zip.parent_id
but the obvious issue is that the join table varies and is only found in
zip.parent_tbl. Obviously, I can select from zip, then step through the
results and select the joined data separately for each zip result. How
can I get these results in one statement? I've tried writing SQL
functions and using subqueries without success. I think I need someone
to point me in the right conceptual direction.

Thanks.

John Gunther
Bucks vs Bytes Inc