The so-called Cartago Conflict was a two-decade long clash between the Terran Hegemony and the Federated Suns over the Jointly-Owned world of Cartago, culminating in the Hegemony's capture of the Federated Suns Terran March capital of Kentares.
By the late 24th century, House Cameron became increasing aware that the limited volume of the Terran Hegemony would eventually mean resource shortages and the collapse of its economy as the raw materials of its worlds ran out. The various Director-Generals realised that the surrounded Hegemony was not sufficiently strong enough to go to war against one Great House to obtain new resources and defend against a backlash from all the others, and that any attempted treaty agreement with the Great Houses would likely force the Hegemony into the equally untenable position of having to sharing some of its jealously guarded technological advances. 
The answer was the Jointly-Owned Worlds proposal developed by young planetary engineer David Ocrassa during the reign of Director-General Margaret Cameron, with the Hegemony negotiating agreements with the neighbouring houses to use the Hegemony's advanced technology to make previously uninhabitable worlds in their realms habitable, in return for ownership of of half each planet's mineral resources and a say in the planet's government. While this would still result in the loss of some closely guarded technologies, the focus specifically on terraforming rather than even more valuable military systems outweighed the disadvantages.
Thanks to the Hegemony's good relations with the Lyran Commonwealth by marriage and relative weakness of the Terrible Tyrants-era Federated Suns, by the beginning of the 25th Century the Hegemony had quickly reached agreements with both realms and transformed twenty such marginal worlds. Proving highly profitable for the realms involved despite occasional political tensions, the program hit its first snag in 2411 when Federated Suns colonists and Terran Hegemony terraforming technicians on Cartago came to blows in response recent economic sanctions taken by the planet's government, with Davion loyalists alleging that the Hegemony oxygen-generating factories were infact stripping the oxygen rather than adding to it. After lives were lost on both sides and conflict showed no sign of abating, the Hegemony accused the Federated Suns of violating the joint-ownership agreement for Cartago and took the planet permanently under its control. 
Angered this action, the Armed Forces of the Federated Suns would launch an attempt to retake Cartago a month later, but the stronger and technologically superior Hegemony Armed Forces succeeded in easily fending off the attack. Over the next two decades the Federated Suns would make several more fruitless military and political attempts to win back Cartago, only serving to increase the tensions between the Hegemony and Suns. By 2431 Director-General Richard Cameron had had enough of the constant battles for the world and choose to send a clear message to the Federated Suns, setting in motion plans to capture the Terran March capital of Kentares. While the AFFS defenders were far more battle-hardened, the superior technology and greater skill of the HAF at the type of warfare mandated by the recently signed Ares Conventions allowed the Hegemony to push the Davion forces off Kentares within six months.
The loss of the far more valuable Kentares would finally eliminate the Federated Suns interest in retaking Cartago, until the collapse of the Star League allowed it to reclaim it. For Richard, that victory proved a great boost to his popularity, allowing him to revise the nomination laws for the position Director-General with minimal complaint. Modifying the laws to give the current holder the right to choose his or her successor without consulting anybody, Richard further weakened the semi-democracy envisioned by James McKenna, making the Hegemony an overt constitutional monarchy under House Cameron control.
For First Prince Simon Davion the conflict would act as blight upon the strength and reputation of the rebuilding Davion realm. The situation would be worsened by the insistence of the Prince of the Terran March that he could deal with the problem alone, spending the next eight years unsuccessfully trying to win back Kentares to no avail. When he finally asked for aid from New Avalon and the other Marches by 2439, the Terran Hegemony's introduction of the BattleMech made the Terran Hegemony's military all but invincible, allowing it to also hold Kentares until the Star League's collapse.
- The Star League, p. 27 "Joint-Ownership of Worlds"
- The Star League, p. 29 "Richard Cameron"
- Handbook: House Davion, p. 28 "New Government, New Challenges"
- House Davion (The Federated Suns), p. 36 "History - Principality - The First Prince"