For Houses Major - the planetary ruling noble dynasties - I tend to simplify my Family Generating rules even further as I am inevitably attempting to construct a lineage that stretches over several centuries.
Usually, I have a date when the dynasty first gained its title. A number of the Rimward dynasties, for example, were established during the Trumer Restoration, the campaigns of Sector Duke Leonid I Trumer that ended the chaos of the Sarkul Wars in 906. 906 is the official date for the establishment of Miazan Subsector, the founding of the Duchy of Miazan and the accession of House Geyukthi as Dukes of Miazan. It also marks the accession of House Mahuran as Counts of Bromus. Obviously, there were antecedents in the family lineages of House Mahuran and House Geyukthi but, prior to 906, these antecedents were just members of the teeming mass of Houses Minor and other functionaries who had found themselves drawn into the orbit of House Trumer and, in particular, the orbit of the man who would become Leonid I, Sector Duke of the RimWorlds.
In the case of the House Geyukthi lineage, with the chronological start point established I pretty much rolled 1D6 and declared that Duke Arkuru I had three siblings, assigned them spouses, and went from there. The width of the page of my notebook pretty much decided the maximum number of descendants per generation, and I kept a close eye on my History of the RimWorlds document to check for events that might lead to major die-offs amongst dynasty members, such as the 3rd Outrim War that devastated the Geyukthis.
The Geyukthis of Miazan are a patrilineal clan - in fact, by default, I tend to construct patrilineal clans as Western European History tends to accept inheritance - of the family name, in particular - as passing through the male line. We accept women taking their husbands' surnames, we accept lines of descent being plotted from father to son, and we are only just beginning to question male primogeniture in the English royal succession. In my notes I have one House Major, House Hikasaku of Gazul Subsector, who practices pure primogeniture - the successor of the first Duke was his daughter, and her husband was bestowed with the honour title of Count, but not Siridar-Count as he did not rule an Imperial County of more than one star system.
When I pretty much pulled the family of Saariki Hassoon out of thin air for my previous post, the dice dealt me a sequence of female characters in all the critical age groups to keep the family viable. Pushing the ages around a few years avoided child brides and child mothers, but pretty much confirmed a matrilineal descent from Liriansa, through Goushansu, to Saariki Hassoon the Marine. I wrote and posted that post at work (a slow day in the data fields) and mulled it over on the way home. The most difficult part of the family tree construction was that I had opted for a vaguely Egyptian naming style and it wasn't immediately obvious which names were male and which female. Other than that, I was suddenly presented with the question of why the 53rd Century Family Trees I had been constructing were so concerned about male lineages when, basically, girls could do anything, including be Marines and Fleet Admirals.
Chagrined, I had a look at House Mahuran, Siridar-Counts of Bromus and the first House Major I had constructed in a couple of decades.
In building this House, I had a character, Count Sakkan III, already extant in my game notes. Looking through my extant family trees, I picked up three female members of House Mahuran who had married into other Houses Major. My usual practice to now has been not to record the ages of females marrying into a House, I have worked under the assumption that their age will be similar to that of their spouse. Working backwards from their spouse's ages, I was able to place these women both generationally, and then temporally, and discovered that the current Count of Bromus had two aunts -sisters of his father - who had become Duchesses of Miazan and Gamelea, respectively. Not bad for a couple of gals from the potato fields of Bromus.
While filling in the generations back to the establishment of the County of Bromus in 906, I realized I had to fit in two more Sakkans, and any number of other holders of the Honour. Somewhere along the way, I discovered that Sakkan I had lingered on as Count for a lot longer than the standard human lifespan. This gave rise to the intrigue about his possible use of anagathics (and possible rumours of a haunted tomb) which, in turn, gave me more scenario ideas.
For those interested in this sort of thing, this Wkipedia article gives a good explanation of what we perceive as the "standard" form of succession, as well as some that are, perhaps, not so familiar.
I particularly like the idea of the Lateral Succession where the Septs of the Clan of the House Major effectively form the Houses Minor of a planetary system, as well as filling its senior military and administrative roles. Upon the death, or retirement, of the current holder of the House Major honour, the heads of the Septs meet in conclave to elect the most suitable member of the Clan to succeed him or her. This person may not necessarily be the head of a particular Sept, but that Sept will gain status for having produced the successful claimant.
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