If the abatement happened on the death of one's grandfather or grandmother, then an assise of mort d' ancestor no longer lies, bur a writ of ayle or de avo; if on the death of the great grandfather or great grandmother, then a writ of besayle or de proavo; but if it mounts one degree higher, to the trefayle or grandfather's grandfather, or if the abatement happened upon the death of any collateral relation, other than those before-mentioned, the writ is called a writ of cosinage, or de consanguineo.
Source: wiktionary