Your character's base attack bonus is the sum of the base attack bonuses from your classes
From the 3.5 PHB, pg59:
Base Attack Bonus: Add the base attack bonuses acquired for each class to get the character's base attack bonus. ... For instance, a 6th-level rogue/4th-level wizard would have a base attack bonus of +6 (+4 for the rogue class and +2 for the wizard class). A base attack bonus of +6 allows a second attack with a bonus of +1 (given as +6/+1 on Table 3-1), even though neither the +4 from the rogue levels nor the +2 from the wizard levels normally allows an extra attack.
BUT you stop gaining BAB from class levels once your character level (total of all class levels) hits 20. Instead you get an "epic" bonus to your attacks at every odd-numbered level after 20th; this increases your attack value, but does not grant additional attacks the way BAB does. This caps characters at 4 attacks from BAB.
From the Epic Level Handbook, pg6 (emphasis mine):
Epic Attack Bonus: Similarly, your base attack bonus does not increase after your character level reaches 20th. However, you do receive a cumulative +1 epic bonus on all attacks at every odd-numbered level beyond 20th... To qualify for any feat that requires a minimum base attack bonus, use the sum of your base attack bonus and epic attack bonus.
(The d20 SRD agrees.)
In this case a 15 fighter / 15 wizard / 10 cleric, assuming the levels were taken in that order, would have a total BAB of +17 (+15 from fighter, +2 from wizard, +0 from cleric); s/he would also have a +10 epic attack bonus, so his/her attacks (before ability scores and other modifiers) would be +27/+22/+17/+12.
An example avoiding the lack of BAB in epic, a 6 fighter / 6 wizard / 6 cleric would have a total BAB of +13 (+6 from fighter, +3 from wizard, +4 from cleric).
Deities are not exempt from this limitation. From Deities and Demigods, pg26:
Levels Beyond 20th: ... Beyond character level 20th, deities' attack and saving throw bonuses increase at new rates. Deities gain a +1 epic attack bonus at 21st level and every other level thereafter, meaning that deity with 40 class levels (on top of the base 20 outsider Hit Dice) has an attack bonus of +40. No deity can have more than four attacks derived strictly from its base attack bonus, so a deity with an attack bonus of +40 gets additional attacks at +35, +30, and +25. ...
Deities essentially always have a BAB equal to 20 from their 20 hit dice as an outsider; class levels always give them the epic bonus instead.