Q.Tamil Nadu 2016 results — what if PR system like Israel? Which party majority? Who forms government? Effect on party relationships?

Recomputing Tamil Nadu's 234 seats by vote share rather than FPTP's constituency-by-constituency count changes the picture sharply.

Using the actual, printed 2016 Tamil Nadu vote shares and applying them proportionally to the 234 Assembly seats (the way Israel's PR system allocates its 120 Knesset seats) gives an approximate picture — note that this is an illustrative calculation, since exact PR results depend on the specific quota/remainder method used, but it is close enough to show the pattern clearly:

Which party would have a majority? Under FPTP, AIADMK's 135 seats out of 234 was a comfortable single-party majority (118+ needed). Under this PR estimate, AIADMK's ~95 seats fall well short of a majority, and so does DMK's ~74 — no single party would command the House alone.

Who would form the government? With no outright majority, AIADMK (as the largest party) would most likely need to build a coalition with one or more smaller parties — plausibly the INC, or several of PMK/BJP/DMDK/CPI/Independents together — to cross the majority mark, rather than governing alone as it actually did.

Effect on relationships between parties. Parties that won zero seats under FPTP despite polling a real share of the vote — PMK, BJP, DMDK, CPI, and Independents collectively over 12% of the vote — would suddenly hold genuine seats and real coalition-bargaining power under PR. This would push Tamil Nadu's politics toward the kind of multi-party coalition bargaining seen in Israel, rather than the two-large-party dominance FPTP currently produces, and would likely make smaller parties significant players in government formation rather than marginal also-rans.