OSPF default route under special circumstance

[Rohrmann Sascha]

Hi,

I have 4 routers:
ISP1                       ISP2
  l                              l
A1                          A2
  l------------------l
B1                          B2

A1 is directly connected to its' on ISP and A2 is directly connected to its' own ISP, too.
A1 and A2 are performing eBGP, iBGP and OSPF.
I already configured all protocols and distributed the default gateway (A{1,2}) for B{1,2}.
For that I created a 0.0.0.0/0 route in the static section  of A{1,2} and filtered it out in the BGP-, OSPF-, and Kernel-table of A{1,2}:

import filter { if net = 0.0.0.0/0 then reject; accept};
export all;

So, basicly A{1,2} should throw this default-route only in OSPF and they should not have the default-route in their own routing-table.
But, unfortunately, A{1,2} actually do have this route in their table.
How do I have to configure my protocols so that A{1,2} do not show this behavior?
In my understandings, routers like A{1,2} should not have a default-route in their routing-table...

My 2nd desire is the following:
A{1,2} should throw the default-route in the OSPF area <only> if the BGP adjacency is reachable and the BGP peer is formed (BGP state should be established).
Is this desire realizable with bird only?
Has somebody already conquered this challenge? Or was it even a problem for anyone?

Thanks in advance.

Sascha
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