Double COUNT & Double LEFT JOIN

[Olexandr Novosad]

I've faced with one obscure situation and finally ask there for explanation, if somebody can…

I have three tables:
CREATE TABLE `a` (
`Id` int(10) UNSIGNED NOT NULL AUTO_INCREMENT,
`bId` int(10) UNSIGNED NOT NULL,
PRIMARY KEY (`Id`),
KEY `ibid` (`bId`)
);

CREATE TABLE `b` (
`Id` int(10) UNSIGNED NOT NULL AUTO_INCREMENT,
`DataVal` int(10) UNSIGNED NOT NULL,
PRIMARY KEY (`Id`)
);

CREATE TABLE `c` (
`Id` int(10) UNSIGNED NOT NULL AUTO_INCREMENT,
`bId` int(10) UNSIGNED NOT NULL,
PRIMARY KEY (`Id`),
KEY `ibid` (`bId`)
);

And execute this query:
SELECT b.Id, COUNT(DISTINCT a.Id) AS c1, COUNT(DISTINCT c.Id) AS c2
FROM b
LEFT JOIN a ON a.bId = b.Id
LEFT JOIN c ON c.bId = b.Id
GROUP BY b.Id;

And use different conditions:
1)
Table a – 1000 records;
Table b – 1000 records;
Table c – 1000 records;
Result:
1000 rows in set (0.03 sec)
2)
Table a – 10000 records;
Table b – 10000 records;
Table c – 10000 records;
Result:
10000 rows in set (0.27 sec)
3)
Table a – 100000 records;
Table b – 100000 records;
Table c – 100000 records;
Result:
100000 rows in set (3.89 sec)

Fine so far…

4)
Table a – 100000 records;
Table b – 100 records;
Table c – 1000 records;
Result:
100 rows in set (4.63 sec)
5)
Table a – 100000 records;
Table b – 10 records;
Table c – 1000 records;
Result:
10 rows in set (42.86 sec)

Last two situations I misunderstand. How it could be?
EXPLAIN looks pretty fine:
+----+-------------+-------+-------+---------------+---------+---------+--------------+------+-------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+--------------+------+-------------+
| 1 | SIMPLE | b | index | NULL | PRIMARY | 4 | NULL | 10 | Using index |
| 1 | SIMPLE | a | ref | ibid | ibid | 4 | bd.b.Id | 100 | |
| 1 | SIMPLE | c | ref | ibid | ibid | 4 | bd.b.Id | 12 | |
+----+-------------+-------+-------+---------------+---------+---------+--------------+------+-------------+

From bad to worse.. I’ve filled up table a as bellow:
+----+-------+-----+
| Id | c1 | c2 |
+----+-------+-----+
| 1 | 7776 | 95 |
| 2 | 7732 | 107 |
| 3 | 7815 | 96 |
| 4 | 7828 | 108 |
| 5 | 30002 | 98 |
| 6 | 7821 | 85 |
| 7 | 7773 | 101 |
| 8 | 7739 | 107 |
| 9 | 7804 | 99 |
| 10 | 7710 | 104 |
+----+-------+-----+
10 rows in set (43.16 sec)
And have changed query:
SELECT b.Id, COUNT(DISTINCT a.Id) AS c1, COUNT(DISTINCT c.Id) AS c2
FROM b
LEFT JOIN a ON a.bId = b.Id
LEFT JOIN c ON c.bId = b.Id
WHERE b.Id=5
GROUP BY b.Id;
Result:
1 row in set (15.06 sec)

Explain looks perfectly:
+----+-------------+-------+-------+---------------+---------+---------+-------+-------+-------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+-------+-------+---------------+---------+---------+-------+-------+-------------+
| 1 | SIMPLE | b | const | PRIMARY | PRIMARY | 4 | const | 1 | Using index |
| 1 | SIMPLE | a | ref | ibid | ibid | 4 | const | 50226 | Using index |
| 1 | SIMPLE | c | ref | ibid | ibid | 4 | const | 98 | Using index |
+----+-------------+-------+-------+---------------+---------+---------+-------+-------+-------------+
but execution time – completely bad.

And there is another one question..
On query without WHERE, EXPLAIN EXTENDED displays 1 warning: Note, 1003, and the same query, but with added database entitle. What does this note mean?