Split list when there is an empty row

Read carefully documentation of Split, you need its friend SplitBy:

SplitBy[a, MemberQ[Null]]

{{{1, 1, 1}, {2, 2, 2}}, {{Null, Null, Null}}, {{3, 3, 3}}}

Here's one way:

Split[{{1, 1, 1}, {2, 2, 2}, {, ,}, {3, 3, 3}},
      ! (MatchQ[#1, {Null ..}] || MatchQ[#2, {Null ..}]) &]

Here two ways to do it using Split.

a = {{1, 1, 1}, {2, 2, 2}, {, ,}, {3, 3, 3}, {4, 4, 4}};

With[{p1 = {{_Integer ..} ..}}, Split[a, MatchQ[{#1, #2}, p1] &]
With[{p2 = {{Except[Null] ..} ..}}, Split[a, MatchQ[{#1, #2}, p2] &]]]

Both give

{{{1, 1, 1}, {2, 2, 2}}, {{Null, Null, Null}}, {{3, 3, 3}, {4, 4, 4}}}

The form using pattern p2 is probably better because it is more general. It will handle

c = {{1, 1, 1}, {2, 2, 2}, { , ,}, {x, y, z}, {4, 4, 4}};

correctly, while the form using p1 stumbles on the sub-list {x, y, z}.

With[{p1 = {{Except[Null] ..} ..}}, Split[c, MatchQ[{#1, #2}, p1] &]]

{{{1, 1, 1}, {2, 2, 2}}, {{Null, Null, Null}}, {{x, y, z}, {4, 4, 4}}}