Place a stone on an empty Go board

C, 212 195 193 181 171 132 103 98 bytes

Saved 1 byte thanks to @FryAmTheEggman, 5 bytes thanks to @orlp

Call f() with the position to play (must be capitalized), and it prints out the resulting board.

i;f(char*p){for(i=380;i--;)putchar(i%20?i^20*atoi(p+1)+64-*p+(*p>72)?i%6^4|i/20%6^3?46:42:79:10);}

Try it on ideone.

C (gcc), 132 128 109

i;m;f(char*s){for(i=380;i--;putchar(m?m^84-*s+(*s>73)|(i/20+1)^atoi(s+1)?m%6^4|i/20%6^3?46:42:79:10))m=i%20;}

Ideone

A function that prints the board to STDOUT. Requires the letter coordinate to be capital. Printing in one loop seems to be slightly shorter than the previous nested loop approach.

MATL, 33 bytes

'*O.'19: 6\4=&*Hj1&)Uw64-t8>-&(P)

Try it online!

Explanation

'*O.'    % Push string with needed characters. Will be indexed into
19:      % Push numeric vector [1 2 ... 19]
6\4=     % 1 for values that equal 4 mod 6, 0 for the rest
&*       % Multiply by transposed version of itself with broadcast. This gives
         % the 19×19 board with 0 instead of '.' and 1 instead of '*'
H        % Push 2. This will correspond to 'O' (stone)
j        % Input string, such as 'Q16'
1&)      % Split into its first char ('Q') and then the rest ('16')
U        % Convert to number (16)
w        % Swap, to move 'Q' to top
64-      % Subtract 64. Thus 'A' gives 1, 'B' gives 2 etc
t8>-     % Duplicate. Subtract 1 if it exceeds 8. This corrects for missing 'I'
&(       % Fill a 2 at coordinates given by the number and the letter
P        % Flip upside down, because matrix coordinates start up, not down
)        % Index the string '*O.' with the 19×19 array containing 0,1,2.
         % Implicitly display