Wayne Jacobs was unable to solve the dilemma that did for Stuart McCall as City drew another home blank this afternoon.
Jacobs, in temporary charge of the side, has put his name forward for the vacancy.
But a dour draw against the second-from-bottom team who haven't won for 21 games was hardly the best advert for his chances.
Potential candidates Martin Allen and Russell Slade looked on as the Bantams again failed to deliver at Valley Parade. The wait for the first home win since the clocks went back in October drags on.
City had made a bright start and it might have been a different story if they had scored early.
Peter Thorne, starting his first game since September 1, jabbed wide and Nick Colgan palmed away a cross-shot from Gareth Evans.
Playing wide on the left, Evans had another chance from James Hanson's low cross but clipped over the bar.
But the game drifted away and half-time was greeted with a smattering of boos.
Grimsby, having offered nothing, got a bit more adventurous after the break and Matt Glennon beat away Peter Sweeney's snap-shot.
But City still had the bulk of the chances without really threatening a breakthrough. Thorne should have done better after defender Olly Lancashire slipped, sub Michael Boulding fired straight at Colgan and Hanson put a header wide.
There was plenty of huff and puff but Grimsby held on for an eighth draw in their last 11. The new manager, expected to be named around Wednesday, will inherit that home millstone.
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