For the sake of continuity we will assume Ulthor kills Aeyron in their battle, at the Bloodwater.
-Ulthor and Aeyron finally cross paths at the Battle of the Bloodwater where Aeyron vanquishes his enemy but what would've happened if Ulthor killed Aeyron.
-The two of them fight near to Ulthor's command so the body of Aeyron would not be discovered by his fellow soldiers, I would imagine Ulthor would have his command hoist Aeyron's body onto a horse, paraded around to show their king was dead. However we must factor in that Ser Steffon Bracken watched Aeyron and Ulthor fight so following Aeyron's death he would immediately challenge Ulthor, who would know he wouldn't win. Steffon would murder Ulthor there as I see no way Ulthor beating him, or Ulthor would escape with his men(without the body).
-Steffon would inform the others that Aeyron was dead and the loyalist army would order a full retreat similar to the rebel army running after Ulthor and Nestor where killed. Since Nestor was killed by Samuel, Ulthor would be the sole leader of the rebel army now and his orders would be to continue to chase the loyalist army.
-The loyalists would be led by the Kingsguard though their army would be fractured and motiveless, I could see many lords surrendering to Ulthor and joining him. The loyalist aim would be to escape to King's Landing before Ulthor, who would chase after them relentlessly, with new found ambition Ulthor's men would march through the night as well eventually catching up to the loyalists at the Proudroad in The Crownlands. Similar to the Battle of the Proudroad Jon Darklyn would host 20,000 men to fend off Ulthor and let the rest escape; his tactic will work buying enough time for the remaining 40,000 to escape to King's Landing. Jon Darklyn and all his men are killed in the battle.
-Alerting those at King's Landing, The protocol set by Aeyron takes place, The Bat, Quentyn Tower and several loyal men to the Archer family set seal for Ivica. The KingsPeace attempt to fortify what is left of the city after The Battle of King's Landing and alert the citizens who try to escape the city fearful of another Sack of King's Landing by Ulthor.
-When Ulthor's men arrive at King's Landing he demands for there to not be another sack of the city, aware of what it did to his reputation 5 years ago. Battle ensues but with the depleted defences and damaged gates continuing from the Battle of King's Landing, the loyalist defence is not as strong as it would've been. Ulthor's men break through to King's Landing and against Ulthor's wishes, the common soldiers sack the little stores the city has, but with moderate civilian incidents as many of them have fled to the surrounding villages.
-Ulthor's men emerge victorious with the majority of the loyalist surrendering instead of dying, the Kingsguard would rather die than serve under Ulthor. Edmund survives the battle and Ulthor, surprisingly, offers for him to continue to be a part of the Kingsguard if he swears allegiance to Ulthor. Edmund refuses and he is therefore executed.
-Ulthor sends men to bring Joanna and her children to King's Landing, at where she reveals that the two of them were in love. Ulthor also sends men out to find Nymeria and Larra Archer, unaware of where they are and paranoid that his men killed them similar to how his men killed Queen Syrell and her children. Ulthor is coronated and Joanna is named his queen, the two children they have are legitimised and Ulthor puts Aeyron's head on a spike although Joanna later demands him to take it down.