All three are eligible for registry in the IALHA (International Andalusian & Lusitano Horse Association). Eligible PRE horses can be registered in Spain and Eligible PSL horses can be registered in Portugal.

PARTBREDS
Azteca Andalusian/Lusitano X AQHA or APHA
Spanish Norman Andalusian/Lusitano X Percheron
Hispano Arabe Andalusian/Lusitano X Arabian
Warlander Andalusian/Lusitano X Friesian

Other crosses (Andalusian/Lusitano X Thoroughbred, Warmblood, Saddlebred, Morgan, etc) are considered Iberian Warmbloods or Iberian Sporthorses.

Eligible crosses can be registered with the IALHA as Half-Andalusians/Lusitanos.

Many other registries accept these crosses and have their own registries:

American Azteca International Assoc. AAHIA

Azteca Horse Registry of America

International Azteca Horse Assoc

Spanish-Norman Horse Registry

Hispano Arabe Registry and Assoc. of America

International Warlander Society & Registry

Iberian Warmblood Registry

Iberian Sporthorse Registry

American Sporthorse Registry

Various Color Registries