PAT --example html http://askubuntu.com/page01
ABC
DEF

PAT --example html http://askubuntu.com/page02
GHI
JKL

PAT --example html http://askubuntu.com/page03
MNO
PQR

$ cat page01.txt
ABC
DEF
$ cat page02.txt
GHI
JKL
$ cat page03.txt
MNO
PQR

awk -F/ '/^PAT/{close(file);file = $NF; next} /./{print >> file}' foo

$ head page0*
==> page01 <==
ABC
DEF

==> page02 <==
GHI
JKL

==> page03 <==
MNO
PQR

perl -00ne 's#PAT.*/(.*)n##; open($F,">","$1.txt"); s/ns*(n|$)//g;
            print $F "$_n"' original.txt

perl -00ne 's#PAT.*//(.*)n##; $k=$1; $k=~s#[./]##g;open($F,">","$k.txt");
              s/ns*(n|$)//g; print $F "$_n"' original.txt

askubuntucompage01.txt
askubuntucompage02.txt
askubuntucompage03.txt