'Bingowings" said:

The capital ships were there to retrieve the plans, they knew that the guy who caused the scuffle in the Cantina was on the ship but they needed to be sure he had the plans otherwise they'd be shooting down ships for years on end. They wanted to stop them escaping with something they wanted.

They were there to retrieve the plans alright, but not specifically from Han to begin with. No one really knew Han was even helping Luke and Ben deliver the droids. When that spy informed the storm troopers which docking bay the droids were in, they had no idea Han and the falcon were in it, and Han basted out of tatooine so fast that they ran into the capital ships on patrol, not on route to intercept with prior knowledge. Also, to add to that, no one knew what kind of droid would even have the plans, which is why the storm troopers were asking everyone about their droids, and searching every where for any potential droid. And to further proove that they didn't know who owned the ship , you only have to watch scene where they are searching the falcon on the deathstar. They only said the markings match the ship that blasted it's way out of mos-isley. No where in that movie did anyone say, "Hey look, this is Han Solos ship, We finally got the bastard that had the plans!!" And Han and company were hiding in the Falcon so the empire thought it was abandoned which doesn't make any sense, because they were being monitored when they came out of the Alderan destruction field and forced in via tractor beam.

And yes, those capital ships were only there to stop any ships from leaving Tatooine until they found the plans.

The death star escape debate here is sounding like a broken record now, so it's a moot point. Nothing more can be proven from it.

Back to ESB.... R2 was the one that finally fixed the hyperdrive with a simple turn of the knob. If lando kept trying to find out what was wrong ( on his own ) the Executor would have had the falcon in it's tractor beam.