After Tuolei's death, Wokoutai did two things, and it is widely believed that Wokoutai was annexing the army and property of the Tuolei family.
One thing was that Wokoutai asked Tuolei's widow to instigate Lu Hetiani to marry his eldest son Guiyu. Another thing is that Wo Kuotai asked Lu Hetiani to take out 3 thousand households for his second son Kuoduan.
However, in my personal opinion, this is not really the army and wealth of wokoutai in the annexation of the Touraine system. Why?

(WoKoutai stills)
Instigating Lu Hetiani to be wokoutai's younger daughter-in-law, asking the sister-in-law to marry her son felt a little incestuous. In fact, this was a phenomenon that existed in the early days of slavery society, and the Mongols themselves did not feel that it was incest. (The marital status of the Mongols was very special, and a "marriage snatching" system was still very popular at that time.) When people marry a new daughter-in-law, they hurry to grab it and snatch it back, and this new daughter-in-law is yours. Genghis Khan's wife was robbed by others for 9 months before being snatched back by Genghis Khan. )
If wokoutai did this to annex the property of the tow mine system, this is unjustifiable. First, the Mongols' concept of property is different from that of the Han Chinese. When the Mongols needed property, they generally organized conquests and went elsewhere to grab it, rarely internally. (Especially in the early days, it barely appeared.) It was only in the later period that there were more descendants and fewer conquests that they began to merge with each other. )
In both cases, if you let Lu Hetiani marry your eldest son Guiyu, is it called annexing the property of the Toray clan? Wo Kuotai asked Theradro to marry him, not to bring the sons and property of the Instigator Lu hetianni with him. In fact, when Tuolei died, Tuolei's son Möngke was 23 years old, Kublai Khan was 17 years old, Hulagu was 15 years old, and Ali Bu brother was 13 years old. At that time, these were all adults, so how could they have instigated Lu Hetiani to become a son to Guiyu (26 years old)?
(Stills of Instigator Lu hetiani)
From the words that instigated Lu Hethani to resign (she said, my sons are still young, I have to raise them to adulthood), we can also see that in fact, even if Lu Hetiani married, the property and sons would certainly not follow the past. However, there will be no problem of annexation of mine property.
Then, why did Wokoutai let Lu Hetiani marry Guiyu? In fact, he had two considerations: First, he instigated Lu Hetiani to be particularly capable and educated his four sons very well. And his own son Guiyu is not very successful (Wo Kuotai has always disliked him and has not passed the throne to him), and Wo Kuotai wants to instigate Lu Hetiani to assist his son. Second, at that time, Tuolei died by drinking Wokoutai's "washing sickness water", and Wokoutai felt particularly sorry for instigating Lu Hetiani, and he wanted to use this kind of kiss to compensate her. (Maybe Lu Hetiani didn't think so, but from the perspective of Wokoutai, he thought so.) )
(Takayuki stills)
Let's talk about the annexation of the Tuolei army by Wokoutai. At that time, Genghis Khan left 96 of the 100 thousand households to tow mine. After Tuolei's death, Wokoutai asked Lu Hetiani to take out 3 of them and give them to Kuoduan. 3 out of 96 thousand households to give, the proportion is really too small, can this be called annexation?
It is also common for people to do this. If it is in the Imperial System of the Han People, under the whole world, it can not be the royal land, the coast of the land, and the royal subject. Naturally, the army should be controlled by the emperor. However, as the Great Khan's Wokoutai, he did not have such power. I wanted to divide my son, but I couldn't get anything, so I had to give it to someone else. If 3 out of 96 come out, how can it be called annexation of the army?
In this way, the people who instigated Lu Hetiani's army were still making trouble, and they were not willing to be transferred to Theoduan. In the end, it was lu hetian who came forward himself and persuaded the soldiers of the 3 thousand households, and they agreed to go to The Broad End. Similarly, if the emperor of the Han people encountered such a thing, would those troublemakers still have a life?
Therefore, I think that it is a bit exaggerated to say that Wokoutai annexed the property and army of the Touraine family.
(References: "History of the Yuan", "Secret History of Mongolia")