Power TV, a Kannada news channel, has estimated a minimum of eight and a maximum of 12 Assembly seats for the BJP.
For Congress, it predicted three to six wins in the by-elections and 0 to two seats for Janata Dal (Secular).
Public TV, also a Kannada news channel, predicted 8 to 10 seats for BJP, 1 to 2 seats for JD (S) and 3 to 5 for the Congress.
BTV, another vernacular news channel, estimated the BJP to win 9 to 11 seats, 0 to 2 seats for JD(S) and 2 to 4 seats for the Congress.
Hosakote seat is expected to see a close fight between the Congress and the BJP, according to Power TV and Public TV whereas BTV predicted victory for an independent candidate.
In Bengaluru city, Power TV is expecting the Congress to win the Shivajinagar seat while BTV predicted the BJP to win it. Public TV predicted a close fight between the Congress and the BJP.
According to Centre for voting opinion and trends in election research (CVoter), the BJP is expected to win 12 of the 15 seats contested on Thursday.
It predicted the Congress to win only three seats and said the JD(S) may not win even a single seat.
In 4,185 polling stations, 37.77 lakh electors, including 4,711 service electors, cast their votes on Thursday, the Election Commission said.
On Thursday, the by-elections were held in Athani, Kagwad, Gokak, Yellapura, Hirekerur, Ranibennur, Vijaynagara, Chickballapura, K.R. Pura, Yeshwanthpura, Mahalakshmi Layout, Shivajinagara, Hosakote, K.R. Pete and Hunsur.
As many as 248 candidates, 234 males and 14 females, contested the by-elections for 15 constituencies in the state.
Counting of votes will take place on December 9.
( With inputs from IANS )