What are the various halachic opinions regarding this?
For starters, the L'chatchila (full tefilla b'tzibbur) is to start exactly with the Tzibbur as the Mishna Berura in Biur Halacha 109:1 says
דאפשר דזה לאו תפלת צבור גמורה מקרי מאחר שלא התחיל עמהן בשוה וכמו שכתב הפמ"ג
In Siman 65:35 the Mishna Berura says further that it needs to be exactly at the same time
גם לכתחלה ראוי להתחיל תפלת י"ח עם הש"ץ והקהל בשוה
(M'Pi Hashmuah I have heard people say Reb Moshe said up until 2 minutes after the Tzibuur started is still counted as starting at the same time, but I never was able to find it written anywhere)
R' Moshe Sternbuch (Teshuvos Vehanhagos 1:80) says that in Kelm they were extremely careful to have everyone start exactly together
However, beyond the L'chatchila, R' Shlomo Zalman (Halichos Shlomo 1, 8:7) says that as long the Tzibbur is still davening then it is still counted as Tefilla B'tzibbur.
The option of davening along with the shat"z is mentioned in Shulchan Aruch (109:2) is a machlokes between R' Shlomo Zalamn who says it is considered Tefilla B'tzibbur (Halichos Shlomo 1, 8:41) and R' Moshe who says it isn't (Igros Moshe O"C 3:9)
Lastly, the Chazon Ish seems to be the most lenient one I have found so far. In Orchos Rabbeinu (Chelek 3, Page 208) it says the Chazon Ish holds that as long as even one person who started along with the Tzibbur is still davening, then you can start and still be considered Tefilla B'tzibbur. He even says this could work continuously, meaning you start before one person finishes and someone else starts before you finish and so forth. (Although I have heard that he qualified this would only work until the Shat"z says Kaddish Tiskabel, at which point you can no longer be considered joining the Tefilla B'tzibbur.)