This research assesses the genetic composition of three Arab-derived Spanish horse breeds as an example to highlight the major shortcomings related to genealogical analyses in open populations and to propose approaches useful to deal with this task. The studbooks of three Spanish Arab (SA)-derived horse breeds, Spanish Anglo-Arab (dAA), Hispano-Arab (dHA) and Spanish Sport Horse (dSSH) and those of their parental breeds SA, Spanish Purebred (SPB) and Thoroughbred (TB), totalling 211 754 individuals, were available. The genealogies of the dAA, dHA and dSSH were analysed not only using the corresponding studbook (breed exclusive dataset) but also including the genealogies of the founders from parental breeds (completed dataset). Coancestry analyses revealed that the present SA-derived populations share more genes with the Arab than with the other parental breeds. Effective population size was computed by accounting for migration rates to obtain an equivalent closed-population effective size ((eq)N(e)) of 39.2 for the dAA, 56.3 for dHA and 114.1 for dSSH. The essayed methodologies were useful for characterising populations involving migration. The consequences of the management of the analysed breeds are discussed. The results emphasize the need to include the complete genealogies of the individuals to attain reliable genealogical parameters.