How is the estate of a person who passed away to be distributed, leaving behind a full sister, children of a full sister, children of a paternal half-brother, and two maternal half-brothers?

The method of dividing an inheritance cannot be determined until the heirs are accurately identified, which is available via the aforementioned link. If the deceased left only the relatives mentioned, then the children of the sister and the daughters of the paternal brother receive nothing; because they are not heirs in the first place.

However, if the deceased left behind only a full sister, two maternal brothers, and two paternal nephews, then the inheritance is divided as follows:

The Full Sister: One-half (6 shares out of 12), based on the Almighty's saying: "And if there is only one, she gets half." The Two Maternal Brothers: One-third (4 shares out of 12), equally divided between them (two shares for each), based on the Almighty's saying: "But if they are more than that, they share in one-third." The Two Paternal Nephews: The remainder by residuary inheritance (2 shares out of 12, one share for each brother), based on the Prophet's (peace be upon him) saying: "Give the prescribed shares to those entitled to them; then whatever remains is for the nearest male."

Thus, the inheritance will be divided into twelve shares.