According to APHA:
Breeder's certificates, which are available from the APHA, are issued solely at the stallion owner's discretion. Terms for when the breeder's certificate will be submitted to the APHA vary among stallion owners. Typically, a stallion owner will submit the certificate when:
1. The stud fee has been paid;
2. The mare is pronounced in foal;
3. The mare is picked up by the mare owner;or
4. A live foal is produced.
Essentially, breeder's certificates are the stallion owner's protection against default on the part of the mare owner. For instance, if the mare owner fails to pay all necessary fees, the stallion owner can withhold the breeder's certificate so the mare owner cannot register his or her foal until all fees are paid in full.
Likewise, the mare owner should have a signed stallion contract to ensure that the stallion owner fulfills his or her end of the agreement.
Not sure about other clubs or countries rules and regs though.
ďTo see the wind's power, the rain's cleansing and the sun's radiant life, one need only to look at the horse."