Golfscript, 27 characters
" "9*"*"9,{n\.4$>\.+)"0"*}%
The resulting tree looks like this:
*
0
000
00000
0000000
000000000
00000000000
0000000000000
000000000000000
00000000000000000
A version which uses the height parameter only once is one character longer:
9." "*"*"@,{n\.4$>\.+)"0"*}%
And to readReading the height from stdin (with input "10" to generate the example tree), we have to use one additional character for a total takes the same amount of 29characters (28):
~(.,)" "*"*"@,{n\.4$>\.+)"0"*}%