Technically, Outremer is the word used in Seraean circles to refer to any of their colonies; i.e. territory that is politically affiliated with the Empire, but outside of its borders proper. However, the word is usually used to refer to only the most recent expansions, so the earliest two satrapies are often not considered part of Outremer proper. The attached map is a cut and paste of a section of my big sector map, with the satrapies marked and labeled, and with Seraean space lanes put in as well. First, I'll describe each of the satrapies at a reasonably high level (considering that I've only developed systems so far for one of them) and then I'll talk a bit about the space lanes.
Vorgan Than Viceroyalty is the very first "colony" of the Seraeans and their Idacharian allies. Initially, the entire reason that the Seraeans turned their attention westward from their own borders into the scattered New Alderamin sector was that scattered settlements of Idacharians were already here ahead of them, and they invited the Seraeans to help them capture Arsallum. To the Idacharians and their Old Ones cult, closely allied with the Shadow Cult of the Seraeans themselves, Arsallum was a pilgrimage site, an important part of their religious history from the time of the Old Kingdoms, prior to the establishment of the Marian Empire. It had turned extremely heretic, helped spawn the abominations that are the Cyber-liches, and was under their control. With the help of the Seraean military might, the Idacharians conquered Arsallum, pushed the cyber-liches back into what is today the Voormellei Confederation (and inadvertently laying the seeds for their later alliance with the Grand Dukes of the Carrick Grand Marches) and established the very first of the Imperial colonies. Eventually, the Vorgan Than Viceroyalty, ruled by a Viceroy (by definition) grew to encompass four systems, and started to diverge culturally somewhat from the Imperial center. As their interests and concerns were far from Phovos Mal, they developed an unruly, independent streak, which was later to explode following the declaration of various Umbral Crusades, many led by the so-called Free Heathens, who desired even greater autonomy and independence from Imperial control.
However, the wars with the Cyber-liches had been brutal, Pyrrhic affairs, and these shadow knights were looking to establish their own power bases where they could rule absolutely. They desired softer targets, and the immediate vicinity was not necessarily rife with them. Numerous wars with the Reavers to the south and west of them were fruitless, as holding Reaver worlds was deemed to be impossible; the Reavers were too mobile as a society, and their hit and run raids made short-lived conquest attempts on Tronii T'Kali (2135) futile. Fotta Zonaii (2133) was not only heavily armed and truculent themselves, but they were on reasonably good terms with the warriors of Freeport (2131), but they were also willing to make common cause with the Death Sages of the Voormellei Confederation, who still hated the Seraeans and Idacharians (collectively called The Colorless, or sometimes merely The Heathens.) They were too hard of a target, although diplomacy allowed some of the Shadow Knights to negotiate rights of passage through their system for their Crusader armies.
The next conquest was Lada (1935) which has since been gifted to an Idacharian warlock who styles himself an independent king—but to maintain his position, he also agrees to be a stepping stone further to the west. Lada was an independent nation prior to this, settled by a variety of frontiersmen, but they never managed to maintain a strong position, in part due to continual predation by the Reavers. They were easy targets for the Seraeans, who also made the Reavers fear to prowl through the system.
The Dhangetans are a powerful group squatting fetidly over much of the very center of the sector. An expansion of their rule are the Dhangetans of the Desai Worlds; a splinter group that settled near the Carthen Colonies and the Emerus Marches. This made them the next reasonably large group of systems beyond Lada, the Reavers, and a few strong independent worlds—not great targets for further Seraean expansion, really. But their infamous corruption presented opportunity. Vaaxh-zhu, the Dhangetan emir of the Desai Worlds wanted one of his rivals removed, as well as blocking access to further rivals deeper within Dhangetan space. Offering the Crusaders passage through Fenebruck (1634) and Vorli VI (1631) he betrayed his people and offered conquest to the worlds of the Principality of Tan Kajak, as they later came to be known. These worlds were weakened by internal struggle; both Bernese settlers, and the less savory types that followed in the wake of the Dhangetans had wrangled over the systems for years, and both were not only occupied with fighting each other, but also weakened from decades of doing so. Tan Kajak, the founder of this satrapy, made relatively quick work of both forces, claimed all four worlds in short order, enslaved millions of people (to great profit) and sparked a diplomatic crisis between the Monarchy and the Empire (although inadvertently defused an ongoing diplomatic crisis between the Dhangetans and the Monarchy while doing so.) The old space lane that connected Beodon to Hentau III to Perchta and Kereux was cut off, and only pirates or otherwise desperate travelers use it today.
Other crusaders, seeing the grip Tan Kajak had on ruling his satrapy, decided to set up their own demesnes, and turned south from Fenebruck. The Desai lords had recently abandoned Oerken (1536) in disgust, and the Crusaders agreed that it was a pointless exercise to try and conquer it. But nearby were weak and fractured worlds that fell easily to the Crusaders, becoming the Kingdom of Phatoru Shdor.
When the Revanchists managed to flip the allegiance of the worlds of the Carthen Colony from the Monarchy to the Republic, they also came into direct conflict with Tan Kajak. Overall, this small area is the biggest powder-keg in the entire New Alderamin sector. Although few are truly aware of how sensitive the area is, it is in reality crawling with would-be Gavrilo Princips, and many could-be Franz Ferdinands.
These two satrapies are sometimes not considered part of Outremer, because they were the earliest established, and the other three are the results of much more recent aggression by newer Shadow Knight lords. Surrounded mostly by very strong Bernese colonies, with large populations and strong armies, the Shadow Knights, led by the charismatic and dynamic Lord Kar Tanus VI, father of the current ruler of Thanatos (0733), Kar Tanus VII, found an avenue to a weak and decadent new swath of territory that became the three regions of New Outremer. Cabaea (1337) was a Bernese settled world, but refused to recognize the sovereignty of the Monarch—or more specifically, of their local lords—and declared itself independent. Staffed with a relatively powerful military, it was a hard target for either the Shadow Knights or the Royal Military, either one, but not so strong that it didn't need to look for favors and allies. Tanus negotiated right of passage for a massive Crusader force that swarmed Revanchist world Veile, then Koschei Prime and then Rograde, taking them in quick succession.
Claiming to be repossessing their inheritance on Thanatos, another major pilgrimage site that dates back to the days before the Seraean or Marian Empires, they quickly conquered it as well as a host of nearby systems. In doing so, they encroached upon a local war between the Altairan Ascendancy and various Revanchist colonies; the Crusaders didn't care and enslaved and conquered worlds belong to either with impunity.
This is the Civitas Ordenis Umraci, or Shadow Order State, the bulk of what is usually considered Outremer, and it was once ruled entirely by Kar Tanus VI (his son only rules uncontested today on Thanatos itself, while fractious lords and knights from the rest of the satrapy acknowledge his primacy only reluctantly.
More Altairan worlds were conquered to become the Moaktor Phtok satrapy. This Crusade was devastating to the Altairan Ascendency—both the North and South regions are only seven systems each, while ten systems that were formerly Altairan are now outright ruled by the Seraeans, and two others (Traaknizar 0336 and Katturra 0537) have maintained their Altairan lords, but they have allied themselves formally with the conquerors and turned their backs on the leaders of the Ascendancy. Some of those ten systems had already been recently lost to the Altairans and claimed by the Revanchists, however.
And finally, a couple of systems became the Sarkmina Duchy, by expanding mostly at the expense of Republic colonies; Burislav (0936) and Goll III (0937). Although the expansionist aggression that formed all three of these was the same crusader movement, the various satrapies represent, rather the ability of certain crusader lords to carve out their own demesnes and impose their authority over it more than anything else. Culturally, you would not expect too much of a difference between a Sarkmine world, or one in the Moaktor Phtork or the Civitas—but their allegiance would be to a different lord.
This history also explains the space lanes, to a great extent. Coming from the east, you must pass through the Vorgan Than, then Fotta Zonaii, Lada and Fenebruck, and then either go through the Desai Worlds to reach Tan Kajack, or pass through Cabaea to Veile and the New Outremer conquests.
Notable: the Crusaders went to relatively great pains to avoid confronting the Emerus Marches (and thereby bringing down the wrath of the Monarchy on themselves) or the Takach Kingdom. They were opportunists, not masochists, and challenging powerful groups with many resources was generally avoided, whereas taking easy pickings and weak or conflicted worlds was preferred.