I assembled several Star Trek model kits in the early 1980s, but unfortunately none of them survive today (with one quasi-exception noted below). Most were probably trashed when I moved into my own (small!) apartment around 1990. A few may also have been damaged or destroyed during over-exuberant 80s-era battles. In addition I also created several home-made models using cardboard, aluminum foil, and sundry items found around the house.
8October1983: "Today I returned to one of my favourite past times [sic] -- designing small models of spaceships and then building them out of cardboard, tape, glue and other assorted paraphernalia. Today I built the space pod which brought Kirk back to the Enterprise in both ST:TMP and Wrath of Khan. It is a fairly good replica, I think, except for the front which is a bit flat, not the smooth rounded surface it should be (but is very hard to achieve). I even installed four chairs and a control board to add to the realism. I also began to design a Klingon spacecraft which I intend to make nearly as big as my Enterprise and Reliant. (My space pod is only about 18cm x 9cm x 9cm). I'm also thinking of building the Vulcan spacecraft from the first movie and the Regula space station from Wrath of Khan."
6July1984: "Today I bought the AMT model kit of the old version Enterprise. It looks very nice. I can't wait to do it when I beg back."
3November1984: "Today I bought a 22'' long model of the new-version Enterprise. I've assembled all parts of the ship but I'm going to spray paint the separate sub-assemblies before putting them all together."
14November1984: "Finished the Enterprise today and it looks splendid. I just can't decide if I'm going to put it on a stand or not."
My refit Enterprise does survive in a couple of fuzzy photos probably taken shortly after its completion:
I also constructed the K-9 Space Station from The Trouble With Tribbles. I can't find any photos that include it, but I did find a tiny TOS Enterprise model which, if I recall, came with the station. Here it is circa March 2010: