Step 1: Understanding the Question.
The question asks what field of study thanatology covers. The word comes from the Greek "thanatos", meaning death.
Step 2: Key Concept.
Thanatology is the branch of forensic medicine that studies death in every form: somatic death, cellular death, the signs used to confirm death, and the postmortem changes a body goes through afterward.
Step 3: Detailed Explanation.
Option (1) death in all its aspects: this is the exact scope of thanatology, since it covers how death occurs and every change that follows it.
Option (2) solving paternity of a child: paternity disputes are settled through blood grouping and DNA profiling, a separate topic under medical jurisprudence, not thanatology.
Option (3) identification of the living: identification of a person, living or dead, based on age, stature, fingerprints and similar features is its own distinct branch of forensic medicine.
Option (4) detection of lies: this is the job of polygraphy, which records physiological responses like pulse and skin conductance, and has nothing to do with the study of death.
Step 4: Final Answer.
Thanatology deals with death in all its aspects.
\[ \boxed{\text{Death in all its aspects}} \]