A 3-4 inch varanid would be fine in a 10 gallon, but I would advise a 20 long, and I would advise strongly against doing anything larger than that. Rule of thumb for actual scientists, not the hopelessly anthropomorphizing hobbyists is that STL by STLx2 is roughly the appropriate size for most lizards - Arboreals tend to have different requirements, as do the excessively sedentary ambush predators. Varanids are very hardy creatures and extremely difficult to stress out, I've never heard a first hand report of one being stressed to death, so you CAN give it a large enclosure if you so desire. Personally I believe in moving things to ever increasing cage sizes as they grow. My largest, a 5 year old female just shy of 4' STL began as a 6 inch hatchling in a 20L, and moved to a 40Gallon by the time she was 10 inches long (about 5-6 weeks). She remained in there until 15 (roughly 2 months), when I moved her to a 55Gallon, and after she reached 19 inches total length(Another month or so) she got moved into a 3x3x3 enclosure while I constructed her full sized enclosure, which is 4x9x3. She moved into it when she was approaching 30', roughly 6 months later.
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